Questions on Geometry: Bodies in space, right solid, cylinder, sphere answered by real tutors!

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Question 165906This question is from textbook math thenmatics work book

: find the exact volume of a sphere whit the given dimension of the radius of 30inThis question is from textbook math thenmatics work book

: find the exact volume of a sphere whit the given dimension of the radius of 30in
Answer by checkley77(3388)

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V=4/3PIR^3
V=4/3*3.14*30^3
V=12.56/3*27,000
V=12.56*9,000
V=113,040 IN^3 IS THE VOLUME.

Question 165909This question is from textbook math thematics work book

: find the exact volume of a spher with the given dimension of the radius of 4.2m
find the exact volume of a sphere whit the given dimension of the diameter of 12ftThis question is from textbook math thematics work book

: find the exact volume of a spher with the given dimension of the radius of 4.2m
find the exact volume of a sphere whit the given dimension of the diameter of 12ft
Answer by jojo14344(814)

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--------------> working eqn

, Answer
.
--->

---->
, Answer
Thank you,
Jojo

Question 163990: What is the formula to find the square feet of a cylinder?: What is the formula to find the square feet of a cylinder?
Answer by stanbon(18732)

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Area = (circumference of the base)*(height)
= (2(Pi)r)h
================
Cheers,
Stan H.

Question 161646: A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 170 in 2 (see the figure). What are the dimensions of the rectangle?
: A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 170 in 2 (see the figure). What are the dimensions of the rectangle?

Answer by Alan3354(1181)

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I can't see the figure.

Question 158507This question is from textbook
: ANGLE ABC AND ANGLE CBD ARE SUPPLENEBTARY .IT ANGLE CBD MEASURES 70 DEGREES WHAT IS THE MEASURE OF ANGLE ABCThis question is from textbook
: ANGLE ABC AND ANGLE CBD ARE SUPPLENEBTARY .IT ANGLE CBD MEASURES 70 DEGREES WHAT IS THE MEASURE OF ANGLE ABC
Answer by midwood_trail(221)

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If both angles are supplementary, they both add up to 180 degrees.
ABC + CBD = 180
ABC + 70 = 180
ABC = 180 - 70
ABC = 110 degrees.

Question 151970: please help: after a bad day on wall street, mr.magnum lost 30% of his money, but he had $3500 left. how much money did he orginally have at the beginning of the day?: please help: after a bad day on wall street, mr.magnum lost 30% of his money, but he had $3500 left. how much money did he orginally have at the beginning of the day?
Answer by jojo14344(814)

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Let "x"= original money he got
So, if he lost 30%: --------> [x-30%x=$3500], working eqn
Continuing,
x(1-0.30)=3500

----->

x*cross(0.70)/cross(0.70)=cross(3500)5000/cross(0.70)

----------> original money he has
In checking, we'll go back, losing 30%:
$5000-30%($5000)
$5000(1-0.30)
$5000(0.70)
$3500
Thank you
Jojo

Question 151971: please help} solve for m : 4(m-2)=-2(3-m): please help} solve for m : 4(m-2)=-2(3-m)
Answer by stanbon(18732)

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solve for m : 4(m-2)=-2(3-m)
----------
4m-8 = -6+2m
2m = 2
m = 1
========
Cheers,
Stan H.

Question 151965: can you help me with this problem:which ordered pairis not a solution set of y>5x+1? a} (1,5) b} (1,6) c} (1,3) d}(2,5): can you help me with this problem:which ordered pairis not a solution set of y>5x+1? a} (1,5) b} (1,6) c} (1,3) d}(2,5)
Answer by stanbon(18732)

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which ordered pair is not a solution set of y>5x+1?
a} (1,5) b} (1,6) c} (1,3) d}(2,5)
-------------
(1,5) is not a solution because
5 > 5*1+1 is false
============
Cheers,
Stan H.

Question 151966: please help:which property is played in the following equation? (xy)z=x(yz): please help:which property is played in the following equation? (xy)z=x(yz)
Answer by stanbon(18732)

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which property is displayed in the following equation? (xy)z=x(yz)
------
The associative law of multiplication.
Cheers,
Stan H.

Question 151968: i need help: what is the solution set of the equation x/5 + x/2=14?: i need help: what is the solution set of the equation x/5 + x/2=14?
Answer by stanbon(18732)

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what is the solution set of the equation x/5 + x/2=14?
-----------
Multiply thru by 70 to get:
14x + 35x = 5
49x = 5
x = 5/49
============
Cheers,
Stan H.

Question 151969: please help:what is the equation of the axis of symmetry of the graph y=3x^2+12x-2: please help:what is the equation of the axis of symmetry of the graph y=3x^2+12x-2
Answer by stanbon(18732)

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what is the equation of the axis of symmetry of the graph y=3x^2+12x-2
----------------------
The axis of symmetry occurs where x = -b/2a = -12/(2*3) = -2
================
graph(400,300,-10,10,-20,10,3x^2+12x-2)

Cheers,
Stan H.

Question 148503: If a figure forms the base with dimensions of 10ft x 10ft and the pyramids other dimensions are 12ft x 13ft what would the surface area be?: If a figure forms the base with dimensions of 10ft x 10ft and the pyramids other dimensions are 12ft x 13ft what would the surface area be?
Answer by jojo14344(814)

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From what's given, it's a square base pyramid (because of 10 ft x 10 ft dimensions). The base is given, and you gave other dimensions = 12ft, suppposedly should be the height, and 13 ft should be the distance from the tip on the top going down slanted or diagonal on the body in right angle to the base. Sorry, I don't know if you can picture it. But the formula we'll use for Surface Area= (2*base*slanted height) + (base)^2
SA=2*10ft*13ft + 10^2

If you noticed we didn't use the height

. We only need this if we're looking for the Volume

.
Thank you,
Jojo

Question 148488: The diameter of the base of a cylinder measures 4, and the altitude measures 4. In cubic units what is the volume of the cylinder : The diameter of the base of a cylinder measures 4, and the altitude measures 4. In cubic units what is the volume of the cylinder
Answer by mangopeeler07(442)

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Volume of cylinder= pi(r^2)h

This translates into the {area of the base} times the height.

Why? Well, think of a cylinder as a [stack of congruent circles]. The [amount of circles] is the height. Take the area of one circle, and times it by the [amount of circles] or the height of the [stack of congruent circles]. That gives you the volume of the whole [stack of congruent circles].

Anyway, so take pi(r^2)h

and plug in your values. The diameter is 4, so r=2. The altitude, or height, is 4.

Plug all that stuff in and get pi(2^2)4

. Simplify that and get pi(4)4

. Then multiply 4 by 4 and get pi(16)

. Otherwise known as 16pi

.

So your volume would be 16pi

Question 148195: The distance between two places on Earth is 64Kilometers. Find the angle subtended by the arc joining these two pointsnat the center of the earth nearest to Seconds. Radius of Earth is 64000Kilometers.: The distance between two places on Earth is 64Kilometers. Find the angle subtended by the arc joining these two pointsnat the center of the earth nearest to Seconds. Radius of Earth is 64000Kilometers.
Answer by Alan3354(1181)

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The distance between two places on Earth is 64Kilometers. Find the angle subtended by the arc joining these two pointsnat the center of the earth nearest to Seconds. Radius of Earth is 64000Kilometers.
------------------------------
I think the Earth's radius is 6400 km, not 64000
-----
The circumference of the Earth is 2*PI*6400 km (that's for all 360 degrees)
The angle subtended by 64 km is 360*64/(2*PI*6400)
= 0.57296 degrees

Question 145658: Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are 10 inches long?????: Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are 10 inches long?????
Answer by nerdybill(1040)

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For a detailed explanation of apothem and octagon see:
http://www.mathsisfun.com/geometry/regular-polygons.html
.
Use radians NOT degrees...
.
Side = 2 × Radius × sin(π/n)
where
n = number of sides
.
Stuff in the information from the problem:
10 = 2 × Radius × sin(π/8)
5 = Radius × sin(π/8)
5/sin(π/8) = Radius
.
Then, because
Apothem = Radius × cos(π/n)
Apothem = 5/sin(π/8) × cos(π/8)
Apothem = 5cos(π/8)/sin(π/8)
Apothem = 5cos(π/8)/sin(π/8)

Question 145469: Simplify
M4power(N -3power)2power/(M -2power)-3power/(M-4power N 8power/N 8power M -2power)2nd power: Simplify
M4power(N -3power)2power/(M -2power)-3power/(M-4power N 8power/N 8power M -2power)2nd power
Answer by ankor@dixie-net.com(4485)

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M4power(N -3power)2power/(M -2power)-3power/(M-4power N 8power/N 8power M -2power)2nd power
:
Assume you mean:
(M^4(N^-3)^2)/((M^-2)^-3)

----------------
(M^-4*N^8)/(N^8*M)

:
Multiply exponents:
(M^4(N^-6))/(M^6)

----------------
(M^-4*N^8)/(N^8*M)

:
Add/subtract exponents of like terms; n^8 cancels
(N^-6)/(M^(6-4))

-------------
1/M^(1+4))

---------

:
Invert the dividing fraction and multiply
(N^-6)/(M^2)

Question 145467: If a square has deimensions of a square has 3m x 7m waht would the base for the right solid be if it is 8m high, calcualte the surface area for the solid.: If a square has deimensions of a square has 3m x 7m waht would the base for the right solid be if it is 8m high, calcualte the surface area for the solid.
Answer by Alan3354(1181)

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It's not a square if it's 3 x 7.

Question 143956: It takes 150 square feet of wood flooring to cover a 13 by 11 foot room, counting waste. At this rate, how much flooring, to the nearest foot, would it take to cover a 15 by 20 foot room?: It takes 150 square feet of wood flooring to cover a 13 by 11 foot room, counting waste. At this rate, how much flooring, to the nearest foot, would it take to cover a 15 by 20 foot room?
Answer by ankor@dixie-net.com(4485)

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It takes 150 square feet of wood flooring to cover a 13 by 11 foot room, counting waste. At this rate, how much flooring, to the nearest foot, would it take to cover a 15 by 20 foot room?
:
You could us a ratio equation:
:
Let x = amt of flooring required for a 15 by 20 ft room
:
Actual area of the 13 by 11 ft room
13 * 11 = 143 sq ft
:
Actual area of the 15 by 20 ft room
15 * 20 = 300 sq ft
:
150/x

Cross multiply:
:
143x = 150 * 300
:
143x = 45000
x = 45000/143

x = 314.6853 ~ 315 sq ft of flooring required for a 15 by 20 ft room

Question 143957: A new hotel design includes a glass-enclosed cylindrical elevator. A scale model of the elevator is 1 foot high. The actual elevator will be 100 feet tall and 10 feet in diameter. What is the approximate area of a base of the model elevator? Round your answer to the nearest tenth inch.: A new hotel design includes a glass-enclosed cylindrical elevator. A scale model of the elevator is 1 foot high. The actual elevator will be 100 feet tall and 10 feet in diameter. What is the approximate area of a base of the model elevator? Round your answer to the nearest tenth inch.
Answer by vleith(1156)

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Use ratios to find the diameter of the model.
1/100 = x/10

The model diameter is .1
Area of a circle is A = pi*r^2

A = 0.007853975 ft^2}
<BR>

i square foot = 144 square inches<BR>
<IMG SRC=/cgi-bin/plot-formula.mpl?expression=Use+ratios+to+find+the+diameter+of+the+model.%0D%0A%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=1%252F100%2B=%2Bx%252F10%26x=0003+ALIGN=MIDDLE+ALT=%221%2F100+=+x%2F10%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=0.1%2B=%2Bx%26x=0003+ALIGN=MIDDLE+ALT=%220.1+=+x%22+BORDER=0+%3E%0D%0A%0D%0AThe+model+diameter+is+.1%0D%0A%0D%0AArea+of+a+circle+is+%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2Bpi%252Ar%255E2%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+pi%2Ar%5E2%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=d%2B=%2B2r%26x=0003+ALIGN=MIDDLE+ALT=%22d+=+2r%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=r%2B=%2Bd%252F2%26x=0003+ALIGN=MIDDLE+ALT=%22r+=+d%2F2%22+BORDER=0+%3E%0D%0A%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2Bpi%252A%2528d%252F2%2529%255E2%2B%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+pi%2A%28d%2F2%29%5E2+%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2Bpi%252A%2B%2528.05%2529%255E2%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+pi%2A+%28.05%29%5E2%22+BORDER=0+%3E%0D%0A%3CIMG+SRC=%2Fcgi-bin%2Fplot-formula.mpl%3Fexpression=A%2B=%2B0.007853975%2Bft%255E2%257D%250D%250A%250D%250Ai%2Bsquare%2Bfoot%2B=%2B144%2Bsquare%2Binches%250D%250A%257B%257B%257BA%2B=%2B1.1309%2Bsquare%2Binches%26x=0003+ALIGN=MIDDLE+ALT=%22A+=+0.007853975+ft%5E2%7D%0D%0A%0D%0Ai+square+foot+=+144+square+inches%0D%0A&x=0003 ALIGN=MIDDLE ALT=

The model diameter is .1
Area of a circle is A = pi*r^2

A = 0.007853975 ft^2}
<BR>

i square foot = 144 square inches<BR>
" BORDER=0 >A = 1.1309 square inches" BORDER=0 ><BR>
rounded to nearest tenth inch = 1.1square inches
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=143577>Question 143577</A>: <I>A Dodecahedron is composed of how many regular polygons?
<BR>

thanks^_^</I>: <I>A Dodecahedron is composed of how many regular polygons?
<BR>

thanks^_^</I><BR><B>Answer by </B><B>jim_thompson5910(9165)</B><IMG SRC=/images/stars/stars-13.gif> <A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=104502>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=104502">put this solution on YOUR website!</A><BR>Since a dodecahedron has 12 faces, this means that there 12 regular polygons make up a dodecahedron.
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=143582>Question 143582</A>: <I>A dodecahedron is composed of how many reguar polygons??</I>: <I>A dodecahedron is composed of how many reguar polygons??</I><BR><B>Answer by </B><B>Earlsdon(3717)</B><IMG SRC=/images/stars/stars-13.gif> <A HREF=/tutors/aboutme.mpl?userid=Earlsdon><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=104491>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=104491">put this solution on YOUR website!</A><BR>A dodechedron (one of the five platonic solids) is composed of 12 regular pentagons.
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=143546>Question 143546</A>: <I>how much water to fill a fish tank 6feet long 1foot wide 2feet deep</I>: <I>how much water to fill a fish tank 6feet long 1foot wide 2feet deep</I><BR><B>Answer by </B><B>solver91311(1850)</B><IMG SRC=/images/stars/stars-12.gif> <A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=104478>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=104478">put this solution on YOUR website!</A><BR>Multiply the length times the width times the depth to get the number of cubic feet of water. To get the number of gallons of water, do a Google search. Type in "X cubic feet in gallons" replacing the X with the calculated number of cubic feet. Round the answer you get to the nearest gallon because the result of calculations involving measurements should be expressed with no greater precision than the least precise given measurement.
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=142534>Question 142534</A>: <I>The area of the mural is 33 square meters...what is the radius</I>: <I>The area of the mural is 33 square meters...what is the radius</I><BR><B>Answer by </B><B>checkley77(3388)</B><IMG SRC=/images/stars/stars-13.gif> <A HREF=/tutors/aboutme.mpl?userid=checkley77><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=103797>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=103797">put this solution on YOUR website!</A><BR>area=pir^2<BR>
33=3.14*r^2<BR>
r^2=33/3.14<BR>
r^2=10.51 <BR>
x=sqrt10.51<BR>
x=3.24 meters is the radius.
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=117120>Question 117120</A>: <I>What is the radius of a right circular cone with a volume of 800 cubic inches and a height of 12 inches? Round your answer to the nearest hundredth...<BR>
ANSWER CHOICES ARE:<BR>
A) 7.98 inches<BR>
B) 8 inches<BR>
C) 7.98 square inches<BR>
D) 14.14 inches
<BR>

Thanks for helping<BR>
-s.j.a.<BR>
</I>: <I>What is the radius of a right circular cone with a volume of 800 cubic inches and a height of 12 inches? Round your answer to the nearest hundredth...<BR>
ANSWER CHOICES ARE:<BR>
A) 7.98 inches<BR>
B) 8 inches<BR>
C) 7.98 square inches<BR>
D) 14.14 inches
<BR>

Thanks for helping<BR>
-s.j.a.<BR>
</I><BR><B>Answer by </B><B>near2u_28@yahoo.com(2)</B><IMG SRC=/images/stars/iconNewId_16x16.gif> <A HREF=/tutors/aboutme.mpl?userid=near2u_28@yahoo.com><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=103696>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=103696">put this solution on YOUR website!</A><BR>1/3 pi r2h= 800<BR>
pi=22/7<BR>
r=radius<BR>
h=height<BR>
r2=200*7/22<BR>
r2=63 approx.<BR>
r=radius=7.98 cm
</DIV></TD></TR></TABLE><TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=117120>Question 117120</A>: <I>What is the radius of a right circular cone with a volume of 800 cubic inches and a height of 12 inches? Round your answer to the nearest hundredth...<BR>
ANSWER CHOICES ARE:<BR>
A) 7.98 inches<BR>
B) 8 inches<BR>
C) 7.98 square inches<BR>
D) 14.14 inches
<BR>

Thanks for helping<BR>
-s.j.a.<BR>
</I>: <I>What is the radius of a right circular cone with a volume of 800 cubic inches and a height of 12 inches? Round your answer to the nearest hundredth...<BR>
ANSWER CHOICES ARE:<BR>
A) 7.98 inches<BR>
B) 8 inches<BR>
C) 7.98 square inches<BR>
D) 14.14 inches
<BR>

Thanks for helping<BR>
-s.j.a.<BR>
</I><BR><B>Answer by </B><B>checkley71(8405)</B><IMG SRC=/images/stars/stars-13.gif> <A HREF=/tutors/aboutme.mpl?userid=checkley71><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=86194>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=86194">put this solution on YOUR website!</A><BR>V=1/3PIR^2H<BR>
800=1/3*3.14*R^2*12<BR>
800=12.56*R^2<BR>
R^2=800/12.56<BR>
R^2=63.69<BR>
R=SQRT63.69<BR>
R=7.98 INCHES. A) IS THE CHOICE. <BR>

</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=136490>Question 136490</A>: <I>graph the line represented by Y=-3</I>: <I>graph the line represented by Y=-3</I><BR><B>Answer by </B><B>checkley77(3388)</B><IMG SRC=/images/stars/stars-13.gif> <A HREF=/tutors/aboutme.mpl?userid=checkley77><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=99978>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=99978">put this solution on YOUR website!</A><BR>y=-3<BR>
<IMG SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+-3%29+&x=0003 ALIGN=MIDDLE ALT=" graph( 300, 200, -6, 5, -10, 10, y = -3) " BORDER=0 > (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -3).
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=132596>Question 132596</A>: <I>1. A hexagonal right prism has a volume of 500 cubic inches. If the base is a regular hexagon with a side 4 inches. What is the altitude of the prism? Round off your answer to two decimal places.<BR>
2. What is the ratio of the volume of a sphere and a cone with the base diameter of the sphere?<BR>
3.How many cubic inches of material are needed for a solid rubber ball with a diameter of 3 inches? Round off your answer to two decimal places.<BR>
4.What is the approximate area of a segment of circle with a radius 12 meters if the length of the chord is 20 meters?</I>: <I>1. A hexagonal right prism has a volume of 500 cubic inches. If the base is a regular hexagon with a side 4 inches. What is the altitude of the prism? Round off your answer to two decimal places.<BR>
2. What is the ratio of the volume of a sphere and a cone with the base diameter of the sphere?<BR>
3.How many cubic inches of material are needed for a solid rubber ball with a diameter of 3 inches? Round off your answer to two decimal places.<BR>
4.What is the approximate area of a segment of circle with a radius 12 meters if the length of the chord is 20 meters?</I><BR><B>Answer by </B><B>solver91311(1850)</B><IMG SRC=/images/stars/stars-12.gif> <A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=98813>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=98813">put this solution on YOUR website!</A><BR>The volume of a right prism is given by the area of the base times the height (altitude). Since you know the volume, divide it by the area of the base. The area of a regular hexagon in terms of the length of a side is: <IMG SRC=/cgi-bin/plot-formula.mpl?expression=A=%28%283%2Asqrt%283%29%29%2F2%29t%5E2&x=0003 ALIGN=MIDDLE ALT="A=((3*sqrt(3))/2)t^2" BORDER=0 > where t is the length of the side.
<BR>
<BR>

The volume of a right circular cone is <IMG SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29pi%2Ar%5E2h&x=0003 ALIGN=MIDDLE ALT="V=(1/3)pi*r^2h" BORDER=0 > where r is the radius of the base and h is the height. The volume of a sphere of radius r is <IMG SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29pi%2Ar%5E3&x=0003 ALIGN=MIDDLE ALT="(4/3)pi*r^3" BORDER=0 >. The volume of a cone can be re-written as: <IMG SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29pi%2Ar%5E3%28h%2Fr%29&x=0003 ALIGN=MIDDLE ALT="V=(1/3)pi*r^3(h/r)" BORDER=0 >. So the ratio of the volume of a sphere to a cone with a base diameter equal to the diameter of the sphere would be <IMG SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%2F3%29pi%2Ar%5E3%29%2F%28%281%2F3%29pi%2Ar%5E3%28h%2Fr%29%29=4r%2Fh&x=0003 ALIGN=MIDDLE ALT="((4/3)pi*r^3)/((1/3)pi*r^3(h/r))=4r/h" BORDER=0 >
<BR>
<BR>

The formula for the volume of a sphere is in the paragraph above. Use it.
<BR>
<BR>

Construct the perpendicular bisector of the chord. It will intersect the circle center. This forms a right triangle with half the cord as one side and the radius intersecting one endpoint of the cord as the hypotenuse. The angle between the constructed line and the radius through the cord endpoint is <IMG SRC=/cgi-bin/plot-formula.mpl?expression=arcsin%2810%2F12%29&x=0003 ALIGN=MIDDLE ALT="arcsin(10/12)" BORDER=0 >. (10 divided by 12 comes from half the chord divided by the radius) Twice this angle is the central angle defined by the endpoints of the chord. The area of a circle segment, in terms of the radius of the circle and the central angle is:
<BR>
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29r%5E2%28alpha-sin%28alpha%29%29&x=0003 ALIGN=MIDDLE ALT="(1/2)r^2(alpha-sin(alpha))" BORDER=0 > if you calculate <IMG SRC=/cgi-bin/plot-formula.mpl?expression=arcsin%2810%2F12%29&x=0003 ALIGN=MIDDLE ALT="arcsin(10/12)" BORDER=0 > in radians, or <IMG SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29r%5E2%28%28pi%2F180%29alpha-sin%28alpha%29%29&x=0003 ALIGN=MIDDLE ALT="(1/2)r^2((pi/180)alpha-sin(alpha))" BORDER=0 > if you calculate <IMG SRC=/cgi-bin/plot-formula.mpl?expression=arcsin%2810%2F12%29&x=0003 ALIGN=MIDDLE ALT="arcsin(10/12)" BORDER=0 > in degrees. Where <IMG SRC=/cgi-bin/plot-formula.mpl?expression=alpha&x=0003 ALIGN=MIDDLE ALT="alpha" BORDER=0 > is the central angle and r is the radius.
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=117284>Question 117284</A>: <I>what is the surface area of a dome having a base diameter = 4 meters and a height of 2 meters from the center of the base to the tip top of the dome?</I>: <I>what is the surface area of a dome having a base diameter = 4 meters and a height of 2 meters from the center of the base to the tip top of the dome?</I><BR><B>Answer by </B><B>MathLover1(1157)</B><IMG SRC=/images/stars/stars-12.gif> <A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> <IMG SRC=http://www.endaxi.net/mathsci/math.jpg valign=middle> (<A HREF=/cgi-bin/show-question-source.mpl?solution=85304>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=85304">put this solution on YOUR website!</A><BR>Given:
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=diameter+=d=+4+m&x=0003 ALIGN=MIDDLE ALT="diameter =d= 4 m" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=height=h=+2+m&x=0003 ALIGN=MIDDLE ALT="height=h= 2 m" BORDER=0 >
<BR>

the surface area <IMG SRC=/cgi-bin/plot-formula.mpl?expression=A=+2Pi%2Ar%5Bc%5D%2Ah&x=0003 ALIGN=MIDDLE ALT="A= 2Pi*r[c]*h" BORDER=0 >
<BR>

<BR>
first find radius of curvature <IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D&x=0003 ALIGN=MIDDLE ALT="r[c]" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=%28h%5E2+%2B+%28d%2F2%29%5E2%29%2F%282h%29&x=0003 ALIGN=MIDDLE ALT="r[c]=(h^2 + (d/2)^2)/(2h)" BORDER=0 >………....where <IMG SRC=/cgi-bin/plot-formula.mpl?expression=d%2F2=2m&x=0003 ALIGN=MIDDLE ALT="d/2=2m" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=%28%282m%29%5E2+%2B+%282m%29%5E2%29%2F%282%2A2m%29&x=0003 ALIGN=MIDDLE ALT="r[c]=((2m)^2 + (2m)^2)/(2*2m)" BORDER=0 >
<BR>

<BR>
<IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=%284m%5E2+%2B+4m%5E2%29%2F%284m%29&x=0003 ALIGN=MIDDLE ALT="r[c]=(4m^2 + 4m^2)/(4m)" BORDER=0 >
<BR>
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=+8m%5E2+%2F4m%5E1&x=0003 ALIGN=MIDDLE ALT="r[c]= 8m^2 /4m^1" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=+2m%5E%282-1%29&x=0003 ALIGN=MIDDLE ALT="r[c]= 2m^(2-1)" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=r%5Bc%5D=+2m&x=0003 ALIGN=MIDDLE ALT="r[c]= 2m" BORDER=0 >
<BR>
<BR>

Then:
<BR>
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=A=+2Pi%2Ar%5Bc%5D%2Ah&x=0003 ALIGN=MIDDLE ALT="A= 2Pi*r[c]*h" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=A=+2%2A%283.14%29%2A2m%2A2m&x=0003 ALIGN=MIDDLE ALT="A= 2*(3.14)*2m*2m" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=A=+8%2A%283.14%29m%5E2&x=0003 ALIGN=MIDDLE ALT="A= 8*(3.14)m^2" BORDER=0 >
<BR>

<IMG SRC=/cgi-bin/plot-formula.mpl?expression=A=+25.12m%5E2&x=0003 ALIGN=MIDDLE ALT="A= 25.12m^2" BORDER=0 >
<BR>
<BR>
<BR>

</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=115112>Question 115112</A>: <I>how much water is needed to fill a tank 15feet long,9feet wide and 3 feet deep.What is the formula and answer please. Ineed help and so does my 10 year old daughter</I>: <I>how much water is needed to fill a tank 15feet long,9feet wide and 3 feet deep.What is the formula and answer please. Ineed help and so does my 10 year old daughter</I><BR><B>Answer by </B><B>edjones(2391)</B><IMG SRC=/images/stars/stars-13.gif> <A HREF=/tutors/aboutme.mpl?userid=edjones><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=83748>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=83748">put this solution on YOUR website!</A><BR>V=L*w*h<BR>
=15*9*3<BR>
=405 ft^3<BR>
Ed
</DIV></TD></TR></TABLE><HR width=100%>
<TABLE width=100%><TR><TD><A HREF=/cgi-bin/jump-to-question.mpl?question=114345>Question 114345</A>: <I>A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.<BR>
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?<BR>
(C=2pir)
<BR>

>>>>>>>>>>>>PLEASE I NEED YOUR HELP.....THANKS IN ADVANCE</I>: <I>A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.<BR>
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?<BR>
(C=2pir)
<BR>

>>>>>>>>>>>>PLEASE I NEED YOUR HELP.....THANKS IN ADVANCE</I><BR><B>Answer by </B><B>solver91311(1850)</B><IMG SRC=/images/stars/stars-12.gif> <A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=/images/aboutme-small.gif BORDER=0 alt="About Me" VALIGN=MIDDLE></A> (<A HREF=/cgi-bin/show-question-source.mpl?solution=83208>Show Source</A>): <DIV STYLE="font-family: Comic Sans MS;">
You can <A HREF="/cgi-bin/embed-solution.mpl?show=1&solution=83208">put this solution on YOUR website!</A><BR>You don

miles. The first orbit is one mile above the planet, so we know that the diameter of the orbit is D[p]+2

. We had to add 2 because 1 mile of altitude adds 1 mile to the radius, and the diameter is twice that. Now, if we move out to a point 2 miles above the surface, the diameter of the new orbit is D[p]+4

.
We know that the distance travelled in the first orbit is the circumference of the circle with diameter D[p]+2

, or

, and the distance travelled in the second orbit is C[2]=(D[p]+4)*pi

.

Now we can subtract: C[2]-C[1]

miles. Not too far, really, just a little over six and a quarter miles.

Hope this helps,
John

Question 114345: A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?
(C=2pir)
>>>>>>>>>>>>PLEASE I NEED YOUR HELP.....THANKS IN ADVANCE: A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?
(C=2pir)
>>>>>>>>>>>>PLEASE I NEED YOUR HELP.....THANKS IN ADVANCE
Answer by stanbon(18732)

(Show Source):

You can put this solution on YOUR website!
A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?
(C=2pir)
----------------
Lower orbit distance = 2(pi)(r+1) where r is the radius of the unknown planet.
-------------------
Upper orbit distance = 2(pi)(r+2)
-----------------
Difference EQUATION:
2(pi)(r+2)-2(pi)(r+1) = 2(pi)[(r+2)-(r+1)] = 2(pi) miles
==============
Cheers,
Stan H.

Question 114014: A cylinder has a radius of 5 in. If the volume of the cylinder is 250x3.14 in.to the 3rd power, what is the height of the cylinder? : A cylinder has a radius of 5 in. If the volume of the cylinder is 250x3.14 in.to the 3rd power, what is the height of the cylinder?
Answer by checkley71(8405)

(Show Source):

You can put this solution on YOUR website!
vol=pi*r^2*h
250pi=pi*5^2*h
250=25*h
h=250/25
h=10 inches.
proof
250*pi=pi*25*10
250pi=250pi

Question 113723: A satellite makes a circular orbit around a planet of unknown diameter at an altitude of 1 mile above the planet. Then NASA boosted the satellite to an altitude of 2 miles above the planet. In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit? (C=2 pie r)
>>>>>>>>>PLEASE I NEED YOUR HELP, AND THANKS IN ADVANCE: A satellite makes a circular orbit around a planet of unknown diameter at an altitude of 1 mile above the planet. Then NASA boosted the satellite to an altitude of 2 miles above the planet. In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit? (C=2 pie r)
>>>>>>>>>PLEASE I NEED YOUR HELP, AND THANKS IN ADVANCE
Answer by stanbon(18732)

(Show Source):

You can put this solution on YOUR website!
A satellite makes a circular orbit around a planet of unknown diameter at an altitude of 1 mile above the planet. Then NASA boosted the satellite to an altitude of 2 miles above the planet. In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?(C=2 pie r)
---------------
Circumference of 1st orbit:
C = 2(pi)(1/2mi) = pi miles
----------------------
Circumference of 2nd orbit:
C = 2(pi)*1mi = 2pi miles
-----------------------
It travels pi miles further in the 2nd orbit than in the 1st.
========================
Cheers,
Stan H.

Question 112414: on the lot at honest al's used yugo superstore there are 60 yugos. 20 of the yugos have bad engines, 25 have bad transmissions, 15 have bad engines and bad transmissions. if one yugo is selected, find the probability that it has a bad engine or bad transmission. : on the lot at honest al's used yugo superstore there are 60 yugos. 20 of the yugos have bad engines, 25 have bad transmissions, 15 have bad engines and bad transmissions. if one yugo is selected, find the probability that it has a bad engine or bad transmission.
Answer by solver91311(1850)

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You can put this solution on YOUR website!
There is a question of semantics in this problem. The straight-forward answer is that there are a total of 45 Yugos that have either a bad engine or a bad transmission, (20 + 25). So the probability that any selected car will have either a bad engine or a bad transmission is 45/60=3/4

.

On the other hand, the "or" in "bad engine or bad transmission" could be an exclusive or. In other words, meaning a bad engine or bad transmission but not both. If this is the case, then you would have to say that of the 20 cars with bad engines, 15 of them also have a bad transmission, so there are only 5 (20 - 15) that only have a bad engine. Likewise, there are only 10 (25 - 15) that only have a bad transmission. This is 15 (5 + 10) possibilities out of the 60 total cars: 15/60=1/4

.

Common usage of the word "or," which is the inclusive sense as used in the first solution, would lead me to believe that the first answer is the correct one, but the inclusion of the fact that "15 have bad engines and bad transmissions," a fact that is unnecessary unless the "or" were to be taken in the exclusive sense, makes me think the second answer is the desired one. Ask your instructor what was meant.

Hope this helps,
John

Question 112349: the information in this problem is not fictional. according to a gallup poll (2001), 33% of americans agree with the statement " i believe that earth has been visited by extraterrestrials". if 2 americans are independently selected, what is the probability that neither of them agrees with the statement " i believe that america has been visited be extraterrestrials"?: the information in this problem is not fictional. according to a gallup poll (2001), 33% of americans agree with the statement " i believe that earth has been visited by extraterrestrials". if 2 americans are independently selected, what is the probability that neither of them agrees with the statement " i believe that america has been visited be extraterrestrials"?
Answer by rajagopalan(118)

(Show Source):

You can put this solution on YOUR website!
P=Probability that an american agrees with the statement 0.33 then
Q=Probability that an american dont agree with the statement 0.67 then
Probability that both americans dis agree with the statement 0.67x0.67=0.4489
...
q = 0.45 OR 45% Answer

Question 112343: hamlet is trying to guess the password for the homerina's email account. he knows that the password consists of 5 letters from this set {g,o,m,e,r,i,n,a}. how many passwords are possible, if a password may contain repeated letters?: hamlet is trying to guess the password for the homerina's email account. he knows that the password consists of 5 letters from this set {g,o,m,e,r,i,n,a}. how many passwords are possible, if a password may contain repeated letters?
Answer by checkley71(8405)

(Show Source):

You can put this solution on YOUR website!
8*8*8*8*8=32,768 POSSIBLE COMBINATIONS.

Question 112336: wilhelm has 8 different colors of paint. he is going to choose 4 of the colors and blend them to make a new color. how many different blends are possible?: wilhelm has 8 different colors of paint. he is going to choose 4 of the colors and blend them to make a new color. how many different blends are possible?
Answer by checkley71(8405)

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You can put this solution on YOUR website!
8*7*6*5=1680 POSSIBLE COLOR BLENDS.

Question 111623: A regular has an exterior angle which equals 36 degrees.
how many sides has this regular polygon got?: A regular has an exterior angle which equals 36 degrees.
how many sides has this regular polygon got?
Answer by nihat(10)

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You can put this solution on YOUR website!
Each exterior angle in a regular polygon has measure 360/n degrees where n = the number of sides. Since the regular polygon has an exterior angle of 36 degrees then there are 10 sides since 360/10 = 36.

Question 107642: I have a cylinder 48" tall & 30" in diameter. How many gallons will it hold?: I have a cylinder 48" tall & 30" in diameter. How many gallons will it hold?
Answer by jim_thompson5910(9165)

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You can put this solution on YOUR website!
Remember, if the diameter is 30, then the radius is 15

The volume of a cylinder can be found by the formula
V = pi*R^2*H

Now plug in R=15

and

V =

So it can hold about 33,929.2 gallons

Question 103941: I am also having a problem with this.
The diameter of the Milky Way disc is approximately 9x10^20 meters. How lon does it take light, travel at 10^16 m/year to travel across the diameter of the Milky Way?: I am also having a problem with this.
The diameter of the Milky Way disc is approximately 9x10^20 meters. How lon does it take light, travel at 10^16 m/year to travel across the diameter of the Milky Way?
Answer by edjones(2391)

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You can put this solution on YOUR website!
9*10^20/10^16=9*10^4=90,000 yrs

Question 93231: using a lens with a 2 inch focal length [imagine distance], what is the height of the image when the subject is 180 foot high tree that is 600 feet away?: using a lens with a 2 inch focal length [imagine distance], what is the height of the image when the subject is 180 foot high tree that is 600 feet away?
Answer by scott8148(2719)

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You can put this solution on YOUR website!
2"/600'=image height/180' ... h=(2"(180'))/600' ... h=.6"

Question 93229: jimmy works on a farm. one of his jobs is to fill up the liquid fertilizer tanks when the farmer is spreading the fertilizer. each tank is a cylinder with a diameter of 6 ft. and a height of 4ft. if there seven tanks and 1 cubic foot=7.5 gallons of liquid. how many gallons of fertilizer will all the tanks hold?: jimmy works on a farm. one of his jobs is to fill up the liquid fertilizer tanks when the farmer is spreading the fertilizer. each tank is a cylinder with a diameter of 6 ft. and a height of 4ft. if there seven tanks and 1 cubic foot=7.5 gallons of liquid. how many gallons of fertilizer will all the tanks hold?
Answer by checkley75(3393)

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You can put this solution on YOUR website!
V=B*H WHERE B= BASE AREA & H=HEIGHT
V=3.14*3^2*4
V=113.04 CUBIC FT. PER TANK.
7*113.04=791.28 TOTAL CUBIC FEET.
791.28*7.5=5,934.6 GALLONS OF FERTILIZER.

(Show Source):

You can put this solution on YOUR website!
First, find the volume of one cylindrical tank:
V = (pi)r^2h

where: r = radius of the circular base and h = the height of the tank.
Radius = half the diameter.
r = D/2 = 6/2 = 3 ft.
h = 4 ft.
Use (pi) = 3.14

as an approximation.
The volume of one tank is:
V = (3.14)(3)^2(4)

cu.ft. Multiply this by 7 to find the volume of 7 tanks.
V[7] = (7)(113.04)

cu.ft.
If 1 cu.ft = 7.5 gallons of liquid fertilizer, then:
791.28 cu.ft. = (7.5gal/cu.ft)(791.28cu.ft.) gallons.
This equals 5934.6 gallons.
So, the 7 tanks will hold 5934.6 gallons of liquid fertilizer.

Question 93230: find the surface area and volume of a sphere which has a diameter of 48 cm.: find the surface area and volume of a sphere which has a diameter of 48 cm.
Answer by jim_thompson5910(9165)

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You can put this solution on YOUR website!
Since the diameter is 48, the radius is 48/2=24

Surface Area:

Solved by pluggable solver: To calculate Surface area of a sphere

Geometry Surface Area and Volume of 3 Dimensional Figures
The Formula for Surface area Sphere is
Area=4*pi*radius*radius

Hence, The Surface Area of Sphere of radius 24 is 7238.2294656.

For more on this topic, See the lessons on Geometry: Area and Surface Area

Some more is on Surface Area and Volume and Perimeter and Area.

Volume:

Solved by pluggable solver: FIND volume of a sphere

Volume of a sphere V=(4/3)*pi*r^3 = (4/3)*pi*24^3 = 57905.8348032

Question 93132: a pile of sand is in the shape of a cone. if the pile is 4 meters high and has a diameter of 7 meters, how many cubic meters of sand is in a pile?: a pile of sand is in the shape of a cone. if the pile is 4 meters high and has a diameter of 7 meters, how many cubic meters of sand is in a pile?
Answer by checkley75(3393)

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You can put this solution on YOUR website!
V=1/3BH
V=1/3(PI3.5^2)*4 (PI=3.14)
V=1/3*3.14*12.25*4
V=(3.14*12.25*4)/3
V=153.86/3
V=51.29 CUBIC METERS OF SAND.