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

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ok i have ABSOLUTLEY NO CLUE WHAT TO DO I AM SOOO LOST ! PLEASE SOMEONE HELPME!!
Find the radius of the right cylinder shown, in which the height of the cylinder is equal to the diameter.

Think of a tin can.

Surface area = circumference*height + area of the top circle + area of the bottom circle

     |       |        |         |   |            |           |               |            

     S       =    (2**r) *   h   +          *r²         +             *r²

           

           

Since the height equals the diameter, and the diameter equals twice the radius,

the height equals twice the radius, so substitute 2r for h

           

           

           
         
Substitute  for S

           

Divide both sides by 

           

The 's cancel on the left and 6 divided into 150 is 25

              

              

              

Edwin

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150pi=2pir^2+2pir(r)
I presume 150 pi is the surface area
150pi=2pir^2+2pir^2
150pi=4pir^2
divide by 4pi
37.5=r^2
r= sqrt(37.5)
r=6.12

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V = LWH

V = (2L)WH

V = 2*(LWH)


The original volume is LWH, so the new volume is twice that.


So if you double the length, then the volume doubles.

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Volume of hemisphere = 2/3 pi*10^3
volume of cylinder portion = pi*10^2*h
Total volume =


Volume =

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The size of the perimeter of the square ABCD is equal to 100 cm. The length of
the segment MN is equal to 5 cm and the triangle MNC is isosceles. Find the
area of the pentagon ABNMC.

(The picture on that site isn't to scale.  This is.)



The square's perimeter is 100 cm, so each side of the square is 25 cm.
The area of the square is (25 cm)² or 625 cm²

We need to subtract the area of the triangle.  It is a right triangle, and
it isosceles, so MC = CN.  We use the Pythagorean theorem to find MC and CN.

MC² + CN² = MN²
MC² + MC² = 5²
     2MC² = 25
      MC² = 12.5
       MC =  = CN

Area of the triangle = BASE×HEIGHT = MC×CN = × =  = (12.5) = 6.25 cm²

Area of pentagon = Area of square - Area of triangle
                 = 625 cm² - 6.25 cm² = 618.75 cm²

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I won't draw the other one.

Initially the rectangular prism on the left was full of water. 

It measures 2cm×4cm×10cm

Volume = length × width × height = 2cm × 4cm × 10cm = 80cm³

so the volume of water in the original container is 80cm³


The first container into which part of it was poured to a height of h
is a rectangular prism like the original except that it is only
filled to a height of h cm.

Volume of water = length × width × height = 2cm × 4cm × h cm = 8h cm³

The second container into which the other part of it was poured to a height 
of h cm is a cylinder with radius 1 cm.

Volume of water = p × (radius)² × (height) = p(1)²h = ph = (3.14)h

so the volume of water in the cylinder is 3.14h cm³.

           water in original = water in 1st + water in 2nd 
                
                          80 = 8h + 3.14h
                          80 = 11.14h
                          = h
                         7.2 = h

 So the height is 7.2 cm to the nearest tenth of a centimeter.    

Edwin

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find the length of the slant height of a cone with a radius of 5 cm and a surface area of 235.5 cm2
:
Surface area formula: S.A. = , where r=radius, s=slant height
= 235.5
15.7s + 78.54 = 235.5
15.7s = 235.5 - 78.54
15.7s = 157
s =
s = 10.0 cm is the slant height
:
How about this? Did you understand what we did here? C
:
:
PS, you do not want to put brackets around the text!

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a spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. in this process the surface area of the metal is increased by .....times.
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Original SA = 4*pi*10^2 = 400pi sq cm
1000 spheres --> 1/10 the radius = 1 cm
New SA = 4pi*1000 = 4000pi sq cm
--------
The SA is increased by a factor of 10.
--> increased by 9 times
ie, it's 10 times as much, 9 times more.

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20inches = 50.8 centimeters

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i need to sketch this: all points in space 3cm from a point F.
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That's a sphere, center at F, radius of 3 cm.

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What kind of figure is it? It's impossible to solve otherwise.

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Here is a central cross-section.  Each green and red line segment has
length r, the radius of each sphere and the cylinder:


The radius of each sphere and of the cylinder is r 

The height of the cylinder is 4r

Volume of the cylinder = pr²h = p(r)²(4r) = 4pr³


Volume of each sphere = pr³ 

Volume of cylinder - 2·volume of sphere = 36p

4pr³ - 2·pr³ = 36p



4pr³ - pr³ = 36p

Multiply through by 3

12pr³ - 8pr³ = 108p

Divide through by p

12r³ - 8r³ = 108

       4r³ = 108

        r³ = 27

         r = 3

Edwin

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If the radius of a cylindrical container is doubled, how do you change the height of the container so that the volume will stay the same?
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volume is a function of the square of the radius, 2*r --> 4*volume
Volume is a function of height, so the height is divided by 4.

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Find the eccentricity of earth`s orbit,if the minimum distance of the sun from the earth is 147.5 million kms and maximum distance is 152.5 million kms.
**
Assuming the Earth's orbit around the sun is elliptical:
Consider the standard form of an equation for an ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.
For given problem:
center: (0,0)
a=maximum distance of the sun from the earth= 152.5 million kms.
b=minimum distance of the sun from the earth= 147.5 million kms
c^2=a^2-b^2=(152.5)^2-(147.5)^2=1500
c=√1500≈38.73
eccentricity=c/a=38.73/152.5≈0.254

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Volume of cylinder = pi*r^2*h
Volume = 2009.6 cu.in
radius= 8 inches

Volume = pi* 8 ^2 * h 3.14
2009.6 = 200.96 h

h= 2009.6 / 200.96
h= 10 inches

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need to pack round objects into a rectangular box.
The box is a fixed length of 20" and fixed width of 10".
If the part is a round cylinder of 3.5" diameter, how many can I get in the box? If the part is 4.5", how many can I get in the box?
:
Assuming you mean the cylinder has 3.5" diameter and is 4.5" long
Each part will occupy a rectangular area 3.5 by 4.5
If you place two rows of 5, side by side, a total of 10 can be placed in the box

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Height of cylinder = 14-5 = 9 mm
Radius = 2.5 mm
Curved surface area = 2*pi*2.5*9= 45pi
curved surface area of two hemispheres = 2pir^2*2
=4*pi*2.5^2*
=25pi
Total curved surface area of capsule = 45pi+25pi=70 pi mm^2
220mm^2
m.ananth@hotmail.ca

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I am trying to imagine using three flash lights in a ball to light it up without changing the balance of the ball (too much). If the end of each light is at the center, could they be positioned to be equidistant from each other?
If it were just a single plane, then the angle between each would be 120 degrees. How should two be rotated along other planes to have the ends be equidistant in space?
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This is 3 points on a sphere that are equidistant, and have a CG at the center of the sphere.
Any placement of 3 points in space determines a plane, so the 3 points will always be in the same plane, the plane they define. If their CG is the center of the sphere, then the 3 points have to be on an equator (or great circle) of the sphere, so they have to be spaced 120 degrees apart.
That meets the criteria, and gives the maximum distance between any 2 points.
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If you have 4 points, they're the points of a regular tetrahedron.
6 points is the inscribed octahedron.
8 is the inscribed cube.
12 is the icosahedron.
20 is the dodecahedron.
I don't think others are possible.

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what is the exact area of the base of a circular swimming pool with diameter of 16ft?
i tried a=3.14xrxr x is the multiplication symbol
so 3.14 x 8 x 8 and it was equal to 200.96 which is none of the answer choices
**
I think the problem here is that they want the exact area so you must leave the answer in terms of π, because π is an irrational number. So this is what I believe is wanted:
Area=πr^2=π8^2=64π

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The total area of a right circular cylinder is 42 pi.
If the height of the cylinder is 4, find the length of the radius.
:
2() + =
divide by , results:
r^2 + 4r = 21
A quadratic equation
r^2 + 4r - 21 = 0
Factors to
(r+7)(r-3) = 0
the positive solution is all we want here
r = 3 is the radius

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how do you determine the area of the circular base of a cylindrical pillar when given the volume of the pillar. the volume is 14.13 cubic feet.
-----------


You need more info, such at the height.

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r = 3.65 in

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if you convert 45km/h to cm/minute (45*1000*100/60)= 75,000 cm/minute
we get 75,000 cm/minute
area = 6.5 cm^2
Volume = area * L
6.5*75,000 =487,500 cu.cm
=487.5 liters

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question 1:
height = h
radius = r
surface area = the area of the sides of the can plus the area of top and bottom of the can.
area of the top and bottom of the can is equal to 2*(pi*r^2)
area of the side of the can is equal to h*(2*pi*r)
S = surface area of the can.
S = 2*pi*r^2 + 2*pi*r*h

question 2:
you are given that S = 54*pi square centimeters.
you are given that h = 6 centimeters.
you want to find the radius.
the formula used is the same formula you just derived in question number 1.
that formula is:
S = 2*pi*r^2 + 2*pi*r*h
you know h, so substitute for h in the equation to get:
S = 2*pi*r^2 + 2*pi*r*6
simplify to get:
S = 2*pi*r^2 + 12*pi*r
you know the value of S, so substitute for S in the equation to get:
54*pi = 2*pi*r^2 + 12*pi*r
divide both sides of the equation by pi to get:
54 = 2*r^2 + 12*r
subtract 54 from both sides of the equation to get:
2r^2 + 12r - 54 = 0
divide both sides of the equation by 2 to get:
r^2 + 6r - 27 = 0
this is a quadratic equation in standard form.
factor this equation to get:
(r + 9) * (r - 3) = 0
this equation is true if (r+9) = 0 or if (r-3) = 0 or if both are 0.
solve for r+9 = 0 to get r = -9
solve for r-3 = 0 to get r = 3
r can't be negative so your answer has to be r = 3.
let's see if that's true.
your original equation is:
S = 54*pi
the formula is:
S = 2*pi*r^2 + 2*pi*r*h
you now know that:
h = 6
r = 3
the formula becomes:
S = 2*pi*3^2 + 2*pi*3*6
simplify to get:
S = 2*pi*9 + 2*pi*18
simplify further to get:
S = 18*pi + 36*pi
simplify further to get:
S = 54*pi
the value of 3 for r is good.
your answer is:
r = 3 cm

question 3:
you are given that S = 150*pi square centimeters
same formula is used again.
formula is:
S = 2*pi*r^2 + 2*pi*r*h
h = height
r = radius
S = surface area
d = diameter
you are given that the diameter is equal to the height.
you get:
d = h
diameter is equal to twice the radius.
this leads to:
d = 2r
since h = d, this leads to:
h = 2r
we can substitute for h in the equation by replacing h with 2r to get:
S = 2*pi*r^2 + 2*pi*r*h becomes:
S = 2*pi*r^2 + 2*pi*r*2r
simplify this to get:
S = 2*pi*r^2 + 4*pi*r^2
these are now like terms so we can combine them to get:
S = 6*pi*r^2
we are given that S = 150 square cm.
we replace S with 150 to get:
150 = 6*pi*r^2
divide both sides of the equation by 6 to get:
25 = pi*r^2
divide both sides of the equation by pi to get:
25/pi = r^2
take the square root of both sides of the equation to get:
r = +/- sqrt(25/pi)
we can simplify this a little further to get:
r = +/- 5/sqrt(pi)
since r can't be negative, this then becomes:
r = 5/sqrt(pi)
to confirm this is a good number we start over with the additional information that r = 5/sqrt(pi)
our formula is, once again:
S = 2*pi*r^2 + 2*pi*r*h
we replace h with 2r to get:
S = 2*pi*r^2 + 2*pi*r*2r
we combine like terms to get:
S = 2*pi*r^2 + 4*pi*r^2
we know that r^2 = 25/pi, so we can replace r^2 with that to get:
S = 2*pi*25/pi + 4*pi*25/pi
the pies in the numerator and denominator cancel out and we have:
S = 2*25 + 4*25 which becomes S = 50 + 100 which becomes S = 150
That's the number we are looking for, so the value of r = 5/sqrt(pi) is good.

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pi=3,14
area of the cylinder=25
height=12
volume of the cylinder: pi*area squared*height = 3,14(25)²12
volume--> V
V=3,14(25)²12
V=3,14(625)12
V=3,14*7500
V=23550
The volume is 23550cm³

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One picket is 3 inches wide and the space next to it is 2 inches wide. So for each picket a space of 3 plus 2 = 5 inches is requred. How many times does 5 go into (75 feet times 12 inches) of fence?


John

My calculator said it, I believe it, that settles it

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He has access to 3/4 of a circle 6 ft in radius.

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An oil drum has a volume of 14.13 cubic feet and a length of 4.5 feet. What is the diameter?
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for a cylinder


Solve for r
d = 2r

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Not necessarily, the common usage of a "cylinder" (e.g. a four cylinder engine) implies that they have circular bases. Technically, a cylinder can have any base.

http://en.wikipedia.org/wiki/Cylinder_(geometry)

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Volume is length*width*height

Rate of water coming in is 2 cubic feet per faucet.
There are 2 faucets so total amount of water coming in is 4 cubic feet per minute.
We want to know how many minutes it takes for there to be 20 cubic feet.

Divide by 4 on both sides

Therefore, it will take 5 minutes to fill the tub.

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The total surface area of the cylinder is given by the formula:
, where h is the height and r the radius.
Substituting our values for A, r and h we have:
, solving this equation for h we get:
<=> <=> .

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(3,4)

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They are applying the Pythagorean theorem:
a^2 + b^2 = c^2
where
'a' and 'b' are the legs of a right triangle
and 'c' is the hypotenuse (longest side)
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
sqrt(32) = c
5.66 = c

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What's the shape of the dome?

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6 ft = 72 inches
cubic inches
Vol = 139392*pi cubic inches
1 gallon = 231 cubic inches
Vol = 139392*pi/231 gallons
=~ 1895.7 gallons