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

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Question 817535: A tank is in the shape of cylinder 8 feet tall and 3 feet in radius. Find the exact volume of the tank.
Answer by TimothyLamb(850)   (Show Source):
You can put this solution on YOUR website!
v = pi r^2 h
v = pi 3^2 8
v = 226.195 cu.ft
---
Solve and graph linear equations:
www.sooeet.com/math/linear-equation-solver.php
---
---
Convert fractions, decimals, and percents:
http://www.sooeet.com/math/fraction-decimal-percent.php

Question 815838: Cylinder Applications
A certain steel bushing is in the shape of a hollow cylinder 18.0mm in diameter and 25.0mm long, with an axial hole 12.0mm in diameter. F
ind the volume of steel in one bushing.

I need to know how do this thx.

Answer by ewatrrr(11176)   (Show Source):
You can put this solution on YOUR website!
```
Hi,

V =
18.0mm in diameter and 25.0mm long, with an axial hole 12.0mm in diameter
V(of steel) = ( - )
V(of steel) =  mm^3
```

Question 813015: What is the surface area of a cylinder: diameter = 6 yards; height =8 yards
Answer by ewatrrr(11176)   (Show Source):
You can put this solution on YOUR website!
```
Hi,
What is the surface area of a cylinder: diameter = 6 yards; height =8 yards

Surface Area =
```

Question 808310: How do I find the length of a spiral if it is stated as this problem.
The base of a right cylinder can is 24inches and the height is 7 inches. Need to find the shortest possible spiral that winds once from the top to the bottom is pointed on the can so that the bottom of the spiral is directly below the top of the spiral.

Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
How do I find the length of a spiral if it is stated as this problem.
The base of a right cylinder can is 24inches and the height is 7 inches. Need to find the shortest possible spiral that winds once from the top to the bottom is pointed on the can so that the bottom of the spiral is directly below the top of the spiral.
-------------------
The length of the spiral is the hypotenuse of a right triangle.
One leg is the height, 7 inches, and the other is the circumference of the cylinder.

Question 802569: The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.1 cm. Find the length of the wire.
Answer by josgarithmetic(3317)   (Show Source):
You can put this solution on YOUR website!
Radius of the sphere is cm.
VOLUME is cubic centimeters, the same as would be the 0.10 cm diameter rod.

Let y = the length of the rod formed, its volume is

Form the equation ,
Simplify and solve for y.

.
.

-----------------------------------------------------------
The solution used radius as "half of diameter is radius".

Question 801347: What is the height of a cylinder that has the same volume and radius as a sphere of a diameter 12 cm?

Answer by lwsshak3(7679)   (Show Source):
You can put this solution on YOUR website!
What is the height of a cylinder that has the same volume and radius as a sphere of a diameter 12 cm?
***
Volume of sphere=4πr^3/3, r=radius
volume of cylinder=πr^2h, r=radius, h=height
..
r=6
4πr^3/3=πr^2h
h=4r/3=24/3=8
height of cylinder=8cm

Question 772989: Find the dimensions of a rectangular prism with a volume of 162 cubic m if the width is 1/2 the length and the height is three times the width.
Answer by pakhi(24)   (Show Source):
You can put this solution on YOUR website!
A rectangular prism is one which has two rectangles as its two end faces.
Volume of a rectangular prism is given by the formula
Volume(V) = Area(A) of one of its rectangles * Height(H) of the prism
Let the length of the rectangle be 'L' meters
Let the width of the rectangle be 'W' meters
Then the area(A) of the rectangle is = length * width = LW square meters
But from the problem we find that W = (1/2)L
Also the height(H) of the prism = 3W = 3*(1/2)L = (3/2)L
So the volume(V) = A * H = L * (1/2)L * (3/2)L = (3/4)L^3
But V = 162 cubic meters
So (3/4)L^3 = 162
or L^3 = 162 * (4/3) = 54 * 4 = 2 * 27 * 4
or L * L * L = 2 * 2 * 2 * 3 * 3 * 3
or L = 6 meters
So W = (1/2)L = (1/2)6 = 3 meters
So H = (3/2)L = (3/2)6 = 9 meters
Therefore the dimensions of the rectangular prism is
Length = 6m
Width = 3m
Height = 9m

Check: V = A * H = L * W * H = 6 * 3 * 9 = 162

Question 771777: A bowl is designed by revolving completely the area enclosed by y = x^2- 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?
Answer by solver91311(18785)   (Show Source):
You can put this solution on YOUR website!

is a parabola with vertex at . is the horizontal line that passes through and that intersects the parabola, in the desired interval, at .

It will be convenient to write as a function of :

Rotate the parabola, then consider a thin disk with radius . The volume of this disk is

Integrate from -1 to 3

John

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

Question 768344: a spherical ball of maximum size is fit into a cylindrical vessel of radius 5 units and height 5 units.the ratio of the volume of the sphere to that of the cylinder is.
Answer by mananth(13127)   (Show Source):
You can put this solution on YOUR website!
Volume of sphere =
Volume of cylinder =

Ratio of volumes =
But h=2r
Ratio =

=
=

Question 764480: find the surface area of a cone with its radius 3.11 and its length 2.25? find the surface area ?
Answer by Cromlix(2315)   (Show Source):
You can put this solution on YOUR website!
Slope = 3.83cm.
Surface Area of a cone = (Pirs) + (Pir^2)
= (Pi× 3.11×3.83) + (Pi×3.11^2)
= 67.81cm^2
Hope this helps.
:-)

Question 760717: if Length of the cylinder increases by 3times..then area decreases by how much?
Answer by tommyt3rd(3721)   (Show Source):
You can put this solution on YOUR website!
Is the volume to be held constant?
What needs to be done is not clear to me from the given information please repost with a clear and complete question :)

Question 763128: A cube & a sphere have equal volumes. find the ratio of the radius of the sphere to an edge of the cube?
Answer by ramkikk66(540)   (Show Source):
You can put this solution on YOUR website!
Let the radius of the cube be 'r' and edge of the cube be 'd'
Volume of cube = d^3
Volume of sphere = = (approx)
Given that both volumes are equal
d^3 = 4.19*r^3
r^3/d^3 = 1/4.19 = 0.2387
r/d = = 0.6203 (approximately)

Ratio of radius of sphere to edge of cube =
:)

Question 757981: Suppose three spherical balls of wax with radius r are packed in a cylinder also with radius r and the balls are melted down. To what depth will the cylinder be filled. The answer needs to be in terms of r. I am totally stumped. Thank you
Answer by ankor@dixie-net.com(16527)   (Show Source):
You can put this solution on YOUR website!
Suppose three spherical balls of wax with radius r are packed in
a cylinder also with radius r and the balls are melted down.
To what depth will the cylinder be filled.
The answer needs to be in terms of r.
:
Find the vol of the three balls in terms of r
V(r) = 3 * *
Cancel the 3
V(r) = cu/units is the volume of the wax
:
let d = the depth of the wax in the cylinder when melted
=
divide both sides by
d = 4r units is the depth

Question 756701: A cylindrical can of orange concentrate has a diameter of 6 cm and a height of 12 cm. The instruction on the can are to mix the orange with 3 cans of water.
a) Will the mixture fit into a cylindrical jug with diameter of 10cm and height 20cm?
b) How high would a jug with diameter 10cm have to be, to hold the mixture?

Answer by Cromlix(2315)   (Show Source):
You can put this solution on YOUR website!
Volume of concentrate can = Pi*r^2*h
= Pi*3^2*12
= 339.29cm^3
Volume of three concentrate cans = 1017.88cm^3
Total = 1357.17cm^3
Volume of cylindrical jug = Pi*r^2*h
= Pi*5^2*20
= 1570.8cm^3
a)Therefore, yes the concentrate + water will fit
in the jug.
b)The total quantity of liquid = 1357.17cm^3
Pi* r^2* h = 1357.17cm^3
Pi* 5^2* h = 1357.17cm63
h = 1357.17cm^3/Pi * 25
h = 17.3cm.
Therefore this is the height required to
hold the mixture in a jug with diameter 10cm.
Hope this helps.
:-)

Question 755565: A sphere has a radius of 8 inches. What is the surface area of the sphere? Round your answer to the nearest whole number.

Answer by lenny460(914)   (Show Source):
You can put this solution on YOUR website!
A sphere has a radius of 8 inches. What is the surface area of the sphere? Round your answer to the nearest whole number.

Surface area of a sphere = 4(pi)r^2
Let pi be 22/7

Therefore:
4 * 22/7 * 8 * 8
(4 * 22 * 8 * 8) / 7
5632 / 7 = 804.57
805 sq inches

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 754249: Larry is building a cylindrical silo that must have a volume of 65m3. the height of the silo must be 6 meters, what is the radius?
Just trying to figure this out. And I keep messing up.

Thanks Jasmine

Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(643)   (Show Source):
You can put this solution on YOUR website!
Larry is building a cylindrical silo that must have a volume of 65m3. the height of the silo must be 6 meters, what is the radius?
formula for the volume of a cylinder is
V = pi*r^2*h
we have
65 = (22/7)*r^2*6 note that pi is represented by (22/7)
multiply both sides of = by 7
455 = 22 *r^2 *6
455 = 132 * r^2
divide both sides of the = by 132
r^2 = 455/132 and
r = sqrt(455/132) = 1.86 m

Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
Larry is building a cylindrical silo that must have a volume of 65m3. the height of the silo must be 6 meters, what is the radius?
----------------

r =~ 1.857 meters
-------------------
Are you my niece Jasmine?

Question 749935: A large cube, 5cm by 5cm by 5cm is painted orange an all six faces, and then it is cut into 125 small cubes, each 1cm by 1cm by 1cm. How many of the small cubes are not painted orange on any face?
(a)125
(b)64
(c)27
(d)24
(e)9

Answer by JoeTaxpayer(186)   (Show Source):
You can put this solution on YOUR website!
This is a giant cube made of 125 small cubes, 5x5x5.
The inner 3x3x3 cube has one layer covering it from any paint, so these cubes are paint-free, 3x3x3 is 27.

Question 747989: A trucks wheel has a diameter of 1 m and a cars wheel is half this. How many times does the trucks wheel turn in 1 kilometer ? Predict how many times the cars wheel turns in one kilometer.
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
A trucks wheel has a diameter of 1 m and a cars wheel is half this. How many times does the trucks wheel turn in 1 kilometer ?
It moves m per rev
# of revolutions = 1000/pi
-------
Predict how many times the cars wheel turns in one kilometer.
We don't predict, we calculate.
2x as many = 2000/pi

Question 747351: If I took a plain sheet of paper (8 1/2 x 11") and folded it to make a cylinder length wise and then width wise, which cylinder would have the most volume.
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(3317)   (Show Source):
You can put this solution on YOUR website!
Lengthwise: 2*pi*r=8&1/2
r=(8&1/2)/(2*pi)
volume=pi*r^2*11
volume=pi*((8&1/2)/(2*pi))^2*11
volume=
which is smaller than widthwise way.

Widthwise: 2*pi*r=11
r=11/(2*pi)
volume=pi*r^2*(8&1/2)
volume=pi*(11/(2*pi))^2(8&1/2)
volume=
, which is bigger than the lengthwise way.

Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
If I took a plain sheet of paper (8 1/2 x 11") and folded it to make a cylinder length wise and then width wise, which cylinder would have the most volume.
---------------
Vol of the taller cylinder = pi*4.25^2*11
Vol of the shorter one = pi*5.5^2*8.5
Compare them.

Question 746738:
Answer by lenny460(914)   (Show Source):
You can put this solution on YOUR website!
Where is your question ?

Question 736378: If radius of a sphere is doubled how many times its volume is increased
Answer by ankor@dixie-net.com(16527)   (Show Source):
You can put this solution on YOUR website!
The volume of a sphere is V =*
r is doubled: = 8 times

Question 734820: suppose you double the radius of a right cylinder
a how does that affect the lateral area?
b how does that affect the surface area?

Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
suppose you double the radius of a right cylinder
a how does that affect the lateral area?

r^1 --> 2x the Lateral Area
--------
b how does that affect the surface area?
Area of ends = pi*r^2
r^2 --> 4x the area of the ends
The total surface area is the sum of the LA and the 2 ends
-----------------

Question 730292: A cylinder of radius of 10cm. It already contains water to depth of 15cm. A metal sphere with volume 900cm^3 is placed in the water. Calculate the height that the water level rises
Answer by ankor@dixie-net.com(16527)   (Show Source):
You can put this solution on YOUR website!
A cylinder of radius of 10cm.
It already contains water to depth of 15cm.
A metal sphere with volume 900cm^3 is placed in the water.
Calculate the height that the water level rises
:
Find the vol of water in the cylinder
V =
V =
V = 4712.4 cu/cm of water
:
Find the total volume of the water and the sphere
4712.4 + 900 = 5612.4 cu/cm
:
Find the height (h) of the water when displaced by the sphere
= 5612.4
h =
h = 17.8647 cm is the height
:
;
Check this by finding the vol of the water between 17.8647 - 15 = 2.8647cm
V =
V = 899.97 ~ 900, the vol of the sphere

Question 727397: a billiard ball is inscribed in a plastic cubical box having a volume of 2744 mm^3. what is the ratio of the billiard ball to that of the volume of the plastic cubical box
Answer by KMST(2478)   (Show Source):
You can put this solution on YOUR website!
The diameter of the ball is the same as the width of the box, and 2 times the radius.
The formula for volume of a sphere says that a ball of the radius
has a volume of

A cube-shaped box of inside width has an inside volume of

The ratio of the volumes is
--> -->
The sizes of ball and box do not matter.
As long as the ball fits tightly in the box, and the box is cube-shaped, the ratio is the same.

NOTE:
If you are curious, and that would make the diameter of your billiard ball 14mm.
That is way too small, marble size.
I did not use a calculator to find

I just divided 2744 by 2, by 2, by 2, and by 7 to get 49 and realize that the prime factorization is

so I knew that

Question 718108: How long wold it take a sample of Am-241 to reduced to 25% of its original value?
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
How long wold it take a sample of Am-241 to reduced to 25% of its original value?
-------------------
Two (2) times its half-life.

Question 714551: How many gallons are in a cylinder with a diameter of 8.5 inches and height of 8.5 inches?
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
How many gallons are in a cylinder with a diameter of 8.5 inches and height of 8.5 inches?
-------------
r = d/2
cubic inches
convert to gallons

Question 712399: What is the volume of a cylinder
radius = 6cm and
height = 7cm, using pi = 3.1?

Answer by stanbon(60778)   (Show Source):
You can put this solution on YOUR website!
What is the volume of a cylinder
radius = 6cm and
height = 7cm, using pi = 3.1?
----
Volume = (area of base)(height)
---
V = (3.17*6^2)(7)
V = 798.84 cu. cm.
=======================
Cheers,
Stan H.
=======================

Question 704571: The radius of a sphere and of a cylinder are the same. The diameter of the sphere and the height of the cylinder are also the same and are twice the length of the radius. If two cones are formed within the cylinder, as shown in the diagram, then the volume of the sphere is equal to which of the following?
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
The radius of a sphere and of a cylinder are the same. The diameter of the sphere and the height of the cylinder are also the same and are twice the length of the radius. If two cones are formed within the cylinder, as shown in the diagram, then the volume of the sphere is equal to which of the following?
---------------
There's no diagram, and nothing follows.

Question 702749: an indoor roller skating rink with an area of 1500 sq yd. has a concrete flooring 3 in. thick. Find the amount of concrete used in laying the floor.
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
an indoor roller skating rink with an area of 1500 sq yd. has a concrete flooring 3 in. thick. Find the amount of concrete used in laying the floor.
-------------
Vol = Area * depth
Vol = 1500 sq yd * 9 sq ft/sq yd * 3 inch * 1 ft/12 inch
Vol = 3375 cubic feet

Question 701067: the size of a brick is 25 cm by 12 cm by 55 cm and its density is the 1.8 by 10^3 kg/m^3.how many trips must a 3 ton dumper carry out to transport 15000 bricks to a constrution site?

Answer by mananth(13127)   (Show Source):
You can put this solution on YOUR website!
Volume of brick = 0.25m * 0.12m * 0.55m = 0.0165 cu.m
volume of 1 brick = 0.0165 cu.m
density = 1.8*10^3 kg/m^3
weight of 1 brick = 0.0165* 1.8*10^3
29.7 kg
15000 bricks will weigh 15000*29.7
=445500 kg
= 445.5 tons
number of trips = 445.5/3 = 1485 trips

Question 699630: If you double the height and radius of a cylinder, why doesn't the surface area double? Thanks!
Found 2 solutions by lwsshak3, htmentor:
Answer by lwsshak3(7679)   (Show Source):
You can put this solution on YOUR website!
If you double the height and radius of a cylinder, why doesn't the surface area double?
**
Because the surface area of the top and bottom varies as the square of the radius, that is, if you double the radius, the surface areas of the top and bottom increase 4 times. Area=πr^2

Answer by htmentor(855)   (Show Source):
You can put this solution on YOUR website!
Surface area of a cylinder

Doubling both the radius, r and the height, h gives

So the new surface area is four times the old surface area

Question 696306: If a circle of radius 6 were cut into 12 equal pieces, How much area would eah piece contain?
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
If a circle of radius 6 were cut into 12 equal pieces, How much area would eah piece contain?
--------------

Divide by 12

Question 696308: How do you find the long leg of this special right triangle given the hypotenuse? (30,60,90)
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
How do you find the long leg of this special right triangle given the hypotenuse? (30,60,90)
-----------------------
The short leg = 1/2 the hypotenuse.
You can use that and Pythagoras.
Or, the long leg = hyp*sine(60)

Question 696304: if a sphere's diameter doubles in size how much larger is the volume?
Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
if a sphere's diameter doubles in size how much larger is the volume?
------------

Volume is a function of the cube of the radius.
2x the radius --> 8x the volume.
---------
"How much larger" ---> 7 times larger, a 700% increase

Question 676228: what is the longest piece of dry spaghetti that will fit in a cylindrical can that has a radius of 3 inches and a height of 14 inches?
Answer by fcabanski(1133)   (Show Source):
You can put this solution on YOUR website!
14 inches. It can't be longer than the can's height, which is 14 inches. The can's radius doesn't matter to the length of the spaghetti.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

Question 670565: Please help me to solve this problem .
A solid steel has a 6 dm diameter and a height of 6 m.How many cubic dm of metal are in the cylinder?

Answer by fafa(13)   (Show Source):
You can put this solution on YOUR website!
First you have to convert the height into dm
so, the height is 60dm
the volume of cylinder is = 3,14 . (1/2 . 6)^2 . 60 = 1695,6 cubic dm

Question 662353: The cube shown here has volume 1000 cm3. If its edges are all doubled in length its new volume will be
Answer by stanbon(60778)   (Show Source):
You can put this solution on YOUR website!
The cube shown here has volume 1000 cm3. If its edges are all doubled in length its new volume will be
----
Original edge length = 1000^(1/3) = 10 cm
----
New edge length = 20
----
New volume = 20^3 = 8000 cm^3
=====================
Cheers,
Stan H.

Question 650764: a cylinder with radius 2 inches and height 4 inches has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder.
bobhilton34@yahoo.com

Answer by ankor@dixie-net.com(16527)   (Show Source):
You can put this solution on YOUR website!
a cylinder with radius 2 inches and height 4 inches has its radius tripled.
How many times greater is the volume of the larger cylinder than the smaller cylinder.
:
Since the radius is squared when you find the volume of a cylinder,
tripling the radius, increases the volume by 3^2 or 9 times
:
You can confirm this on your calc
enter:

and

Question 650148: I need help with a Precalculus problem:
The weight, W, of an object varies inversely as the square of the distance, d, from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find their weight when they are orbiting 400 mi above sea level.

Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(10616)   (Show Source):
You can put this solution on YOUR website!

is called the constant of proportionality
given:
pounds
mi

---------------

The astronaut weighs about 200 pounds

Answer by Alan3354(34679)   (Show Source):
You can put this solution on YOUR website!
The weight, W, of an object varies inversely as the square of the distance, d, from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find their weight when they are orbiting 400 mi above sea level.
---------------
W = k/r^2
220 = k/3978^2
You can solve for k, but it's not necessary.

W = 181.64 pounds

Question 638170: P+2P=-15
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(7480)   (Show Source):
Answer by jim_thompson5910(29613)   (Show Source):
You can put this solution on YOUR website!

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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