Questions on Geometry: Volume, Metric volume answered by real tutors!

Tutors Answer Your Questions about Volume (FREE)

Question 751330: The diameter of a water tower tank is 12ft , and its height is 14ft . What is the volume of water that can be stored in the tank?
Answer by jim_thompson5910(28593)

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V = pi*r^2*h

V = pi*6^2*h ... r = d/2 = 12/2 = 6

V = pi*6^2*14

V = pi*36*14

V = pi*504

V = 504pi <--- Exact Volume in terms of pi

V = 504(3.14)

V = 1582.56 <--- Approximate volume (using pi = 3.14 roughly)

Note: answer is in cubic feet

Question 751278: Jar A can hold 400 candies, and jar B can hold 2,800 candies. If the volume of jar A is 5 inches3, what is the volume of jar B?
Answer by josgarithmetic(1507)

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The volume given for jar A is in units of cubic inches. Already a volume unit, so no need to be confused about different kinds of units or dimensions.

400%2F2800=5%2Fc

where c is the volume in cubic inches for jar B.

The reciprocals are also equal:
2800%2F400=c%2F5

Question 751175: the volume of a prism is 360, the dimensions are doubled by what factor would you multiply by this volume, what is the new volume
Answer by timvanswearingen(103)

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If you're talking about a rectangular prism, then the formula for volume is l x w x h. Since you are doubling each dimension, this means you are doing l*2 x w*2 x h*2. Because multiplication is associative, we can rearrange to get l x w x h x 2 x 2 x 2. So you basically have the original volume (l x w x h) * (2 x 2 x 2) = (l x w x h) * 8. So the volume is increased by a factor of 8.
8*360=2880 cubic units

Question 750848: Help me solve this:
Joni wants to ship a baseball bat. The bat is 2.75 feet long. Joni has three boxes. The dimensions of each box are given below. Which box could Joni use to ship the bat?
A. 0.5 ft, 1.0 ft, 2.5 ft.
B. 1.0 ft, 1.0 ft, 2.0 ft.
C. 1.0 ft, 2.0 ft, 2.0 ft.
D. 1.5 ft, 1.5 ft, 1.5 ft.
I don't understand the measurements. Which number is measuring what? And how do I figure this out?
Answer by rothauserc(206)

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The dimensions of a box are given as
length by width by height
our bat is 2.75 feet long
looks like Joni has four boxes (A, B, C, D) and not one of them is long enough
we could cut the bat in half LOL

Question 750724: A sphere has a volume that is 36(pie) cubic inches. Find the radius.
a 3in
b 6in
c 8in
d 12in
Answer by Cromlix(307)

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Volume of a sphere = 4/3 pi r^3
36 pi = 4/3 pi r^3
36 = 4/3 r^3
27 = r^3
r = 3 inches
Hope this helps
:-)

Question 750429: A ball has a radius of 6cm. Jack puts some balls into a cylindrical tank with a diameter of 24cm containing water. The water level rises 8cm. How many balls are in the tank?
Answer by josgarithmetic(1507)

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The volume of the added balls to the cylinder is pi%2A12%5E2%2A8

.

1 ball has volume of %284%2F3%29%2Api%2A3%5E3

.

The simplest question now to ask is, how many of these 1-ball volumes are in the volume difference found in the cylinder? %28pi%2A12%5E2%2A8%29%2F%28%284%2F3%29%2Api%2A3%5E3%29

%28pi%2A12%5E2%2A8%29%2F%28%284%2F3%29%2Api%2A3%5E3%29

is how many balls.

Question 750479: The volume of a cone is 108(3.14)cm^3. If the area of the base is 81(3.14)cm^2, what is the height ?
Answer by DrBeeee(378)

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The volume of a cone is given by
(1) V = B*h/3 where
(2) B = pi%2Ar%5E2%7C%7C%7C+but+you+given+B+as%0D%0A%283%29+B+=+%7B%7B%7B81%2Api

pi%2Ar%5E2%7C%7C%7C+but+you+given+B+as%0D%0A%283%29+B+=+%7B%7B%7B81%2Api

and
(4) V = 108pi

Substituting (3) and (4) into (1) yields
(5) 108%2Api+=+81%2Api%2Ah%2F3

or
(6) 108 = 27*h or
(7) h = 4
Answer: The height of the cone is 4cm.

Question 750441: What is the volume of a square pyramid with base edges of 20 meters and a height of 30 meters?
Answer by MathLover1(6627)

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The volume of a square-based pyramid is given by
V=%281%2F3%29Ah

where

is area of the base and

is height
if l=20m

V=%281%2Fcross%283%29%29400m%5E2%2A+cross%2830%2910m

Question 750364: A ball has a radius of 6cm. Jack puts some balls in a cylindrical tank with a diameter of 24cm containing water. The water level rises 8cm. How many balls are in the tank?
Answer by ankor@dixie-net.com(15649)

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A ball has a radius of 6cm.
Jack puts some balls in a cylindrical tank with a diameter of 24cm containing water.
The water level rises 8cm. How many balls are in the tank?
:
Let n = no. of balls in the tank
Tank radius = 12 cm
:
Total Ball vol = Tank water volume increase
n( 4%2F3

) =

divide both sides by pi
n( 4%2F3

) =

do the math
288n = 1152
n = 1152/288
n = 4 balls

Question 750349: How many inch cubes Would it take to fill a box if the dimensions are 4x6x18?
Answer by stanbon(57307)

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How many inch cubes Would it take to fill a box if the dimensions are 4x6x18?
----
Assuming you mean 4in by 6in by 18in you get:
--
# of 1 in cubes = 4*6*18 = 432
==================================
Cheers,
Stan H.
=========================

Question 750285: How many cylindrical glasses of base diameter 6.5 cm and height 10 cm can you fill to 1 cm from the top if you have 2-litre carton of orange juice? (1 litre = 1000 cm3)
Answer by josgarithmetic(1507)

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volume of 1 cylindrical glass filled as described , 9%2Api%2A3.25%5E2+

.

You want the whole-number part of highlight%282000%2F%289%2Api%2A%283.25%29%5E2%29%29

Question 750185: Need to calculate the volume of a cistern that is 4.88 mts x 2.45 mts x 4.67 mts x 2.60 mts by a height of 1.60 mts. I thank you very much.
Answer by Alan3354(30993)

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Need to calculate the volume of a cistern that is 4.88 mts x 2.45 mts x 4.67 mts x 2.60 mts by a height of 1.60 mts.
--------------
That's 5 dimensions.
You'll have to give info on the shape.

Question 750157:
Answer by tommyt3rd(514)

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Please repost and to include your question :)

Question 750093: A cube has a volume of 625 cubic centimeters. The volume V of a cube can be represented by the equation s^3 = V. What is the area of a square with the same side length as the cube mentioned?
Found 2 solutions by Alan3354, dkppathak:
Answer by Alan3354(30993)   (Show Source):
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A cube has a volume of 625 cubic centimeters. The volume V of a cube can be represented by the equation s^3 = V. What is the area of a square with the same side length as the cube mentioned?
-----------

----
of each face of the cube

Answer by dkppathak(29)   (Show Source):
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volume of cube=side to power 3
side of cube = cube roots of volume(625)
side of cube = 5 cm
area of square= side square
area= 5x5 = 25 cm square
ans 25 square cm

Question 749671: you have been asked to design a small box. the width is 1 inch more than the depth. length is 3 inches more than the depth. volume is 30 cubic inches. what are the dimensions?
Answer by stanbon(57307)   (Show Source):
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you have been asked to design a small box.
the width is 1 inch more than the depth.
Let depth be "x"
Then width is "x+1"
---
length is 3 inches more than the depth.
And length is "x+3"
----
volume is 30 cubic inches.
x(x+1)(x+3) = 30 in^3
------
x(x^2+4x+3) = 30
x^3 + 4x^2+3x-30 = 30
Solution: x = 2
------------------------
what are the dimensions?
depth = 2 in
width = 3 in
length = 5 in
==================
Cheers,
Stan H.
===================

Question 749177: Mary Ann poured 250 milliliters of fruit punch into each of 13 glasses. how many liters of fruit punch sis she pour
Answer by solver91311(16877)   (Show Source):
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Multiply 250 times 13. Then move the decimal point 3 places to the left.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 749130: A cylindrical oil tank with a radius of 2 meters holds 1,000 cubic meters of oil. What is the approximate height of the tank? Use 3.14 for pi, and round your answer to the nearest meter.

Answer by Alan3354(30993)   (Show Source):
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A cylindrical oil tank with a radius of 2 meters holds 1,000 cubic meters of oil. What is the approximate height of the tank? Use 3.14 for pi, and round your answer to the nearest meter.
==================

Question 749014: if the height of the cylinder is 4.5 centimeters and the volume is 40.5 pie cubic centimeters, what is the length of the diameter of the base ?

Answer by solver91311(16877)   (Show Source):
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So

Solve for and then double the answer.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 749024: Volume of a cone radius is 4 height is 6
Answer by Cromlix(307)   (Show Source):
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The volume of a cone is 1/3 pi r^2 h
1/3 pi 4^2 6
= 100.53 units^3 (2 decimal places)

Question 748339: what is the ratio of the volumes of a larger sphere with a diameter of 20 inches and a smaller sphere with a diameter of 8 inches.
Answer by stanbon(57307)   (Show Source):
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what is the ratio of the volumes of a larger sphere with a diameter of 20 inches and a smaller sphere with a diameter of 8 inches.
-------
Vlarger/Vsmall = 10^3/4^3 = (5/2)^3 = 5^3:2^3 = 125:8
============================================
Cheers,
Stan H.
=================

Question 748238: the ratio of two similar solids are 729m cubed and 125 m cubed. the surface area of the larger solid 324m squared. what is the surface area of the smaller solid?

Answer by lynnlo(4155)   (Show Source):
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Question 748195: What does one thousand centimeters cubed of water fills a -------- -liter?
Answer by Edwin McCravy(8908)   (Show Source):
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What does one thousand centimeters cubed of water fills a --------?

You say "centimeters cubed" but a more appropriate way to say it is "cubic centimeters". But it does indeed mean "centimeters cubed" The fact you must know here is that 1 ml = 1 cm³ That is to say, there is no difference between 1 milliliter and 1 cubic centimeter. We know that 1000 milliliters makes 1 liter. Since a milliliter is a cubic centimeter, we then know that 1000 cubic centimeters makes 1 liter. Edwin

Question 747987: Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 16 feet by 16 feet by 3 inches for a patio if the concrete is $42.00 per cubic yard?
Answer by Alan3354(30993)   (Show Source):
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Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 16 feet by 16 feet by 3 inches for a patio if the concrete is $42.00 per cubic yard?
--------------
Vol = 16*16*1/4 cubic ft = 64 cu ft
1 cu yd = 27 cu ft
---
cost = $42*64/27
cost = $99.56

Question 747837: Find the volume and area of a right circular cylinder of height 3cm and diameter 40cm
Answer by Cromlix(307)   (Show Source):
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Volume of a right circular cylinder
= Pi r^2 h
= Pi 20^2 3
= 3769.9 cm^3
Lateral Surface Area
= 2 pi r h
= 2 pi 20 3
= 376.99 cm^2
Total Surface Area
=2 pi r^2 + 2 pi r h
=2 pi 20^2 + 2 pi 20 3
= 2890.27 cm^2

Question 747248: the dimensions of the larger balloon is twice those of the smaller balloon. if the volume of the smaller balloon is 50 cubic inches, what is the volume of the larger balloon?
Answer by ankor@dixie-net.com(15649)   (Show Source):
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the dimensions of the larger balloon is twice those of the smaller balloon.
if the volume of the smaller balloon is 50 cubic inches, what is the volume of the larger balloon?
:
Find the ratio of the volumes of the two balloons
:

-----------

:

-----------

Cancel like terms and we are left with

Volume of the larger balloon: 8 * 50 = 400 cu/in

Question 746823: The volume of a cylinder is 24 cubic inches. If the height is doubled, what will the new volume be?

Answer by Alan3354(30993)   (Show Source):
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The volume of a cylinder is 24 cubic inches. If the height is doubled, what will the new volume be?
--------
2*24 = 48 cubic in

Question 746495: I have a submarine that consists of a hemisphere, a cylinder, and a cone. The length of the submarine is 17, the radius of the cone, cylinder, and hemisphere is 3, and the slant height of the cone is 5. How do I find the volume of the submarine?
Answer by solver91311(16877)   (Show Source):
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The cone has a radius of 3 and a slant height of 5, so knowing that 3-4-5 is a Pythagorean triple, we can see that the height of the cone is 4. Since the radius of the hemisphere is 3, the depth of the hemisphere must also be 3. 17 minus 4 minus 3 leaves 10 which must then be the height of the cylinder. Calculate the volume of each part of the whole using the formulas for the volume of a cone, cylinder, and hemisphere (1/2 times the volume of a sphere of the same radius). Add the three volumes together.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 746480: The formula for the volume of a cylinder is calculated from the formula v = (pi)r2h. A cylindrical silo is 80 feet high and has a base radius of 200 feet. How much grain does the silo hold?
Answer by Alan3354(30993)   (Show Source):
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The formula for the volume of a cylinder is calculated from the formula v = (pi)r2h. A cylindrical silo is 80 feet high and has a base radius of 200 feet. How much grain does the silo hold?
----------------------

r = 200
h = 80

Question 746450:

Stevens crayon box is 7 cm wide, 2 dm long, and 4cm deep. What is the volume of Stevens crayon Box in cubic centimeters?

Answer by checkley79(3050)   (Show Source):
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V=LWH
V=2*7*4
V=56 cm^3 ans.

Question 746417: please help me solve this question
a solid pyramid of height 40 cm with a square base of sides 30 cm each is put into a cubical tank of sides 40 cm each. the tank is then filled with water. if the pyramid is removed , find the depth of water in a tank.
answer:32.5cm
question is how the answer is coming 32.5cm with this equation?
Answer by Cromlix(307)   (Show Source):
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Volume of a pyramid = 1/3 x Area of base x height
= 1/3 x 900 x 40
= 12000 cm^3
Volume of tank = length x breadth x height
= 40 x 40 x 40
= 64000 cm^3
64000 - 12000 = 52000 cm^3 water left
52000 cm^3 / 40 x 40 = h
h = 32.5cm.

Question 746414: A cylinder has a volume of 19 cm3. If the radius is doubled, what is the volume of the new cylinder?
Answer by tommyt3rd(514)   (Show Source):
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Volume for a cylinder is:

so if radius doubles the new volume is

new volume 19 cm^3

:)

Question 746299: How to find the volume of a hollow hemisphere
Answer by Cromlix(307)   (Show Source):
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The volume for a sphere is 4/3 pi r^3. r = radius.
Take the value and then halve it.

Question 746080: what is the volume if the height is 18 and the diameter is 6?
Answer by Alan3354(30993)   (Show Source):
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what is the volume if the height is 18 and the diameter is 6?
----------
Volume of what?

Question 746061: The volume of a cone is 127 cubic inches and the height of the cone is 6.0 inches. What is
the radius of the base to the nearest tenth
Answer by Alan3354(30993)   (Show Source):
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The volume of a cone is 127 cubic inches and the height of the cone is 6.0 inches. What is the radius of the base to the nearest tenth
----------------

Question 745574: If you have a cone and a cylinder with the same base and same height, and the cone holds 30mL of water, how much water would the cylinder hold?
Answer by Cromlix(307)   (Show Source):
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Vol of cone = 1/3 pi r^2 h
Vol of cylinder = pi r^2 h
so the volume of the cylinder
must be 90 mL ( 3 x 30 mL)

Question 745086: If a pool has a volume of 400m, a length of 20m and a breath of 10m. What is its depth?
Answer by Alan3354(30993)   (Show Source):
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If a pool has a volume of 400m, a length of 20m and a breath of 10m. What is its depth?
------------
400 m is not a volume.
400 cubic meters is volume.
----
Volume = L*W*H
400 = 20*10*H

Question 744763: a
cylindrical tennis
ball container can
contain maximum
three ball stacked
on one another.the
top and bottom ball
also touch the lid
and the base of the
container
respectively if the
volume of a tennis
ball is 240 cm,then
what is the volume
of the container?
Found 2 solutions by MathLover1, mananth:
Answer by MathLover1(6627)   (Show Source):
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given:
cylindrical tennis ball container can contain maximum three ball stacked
on one another
the top and bottom ball also touch the lid and the base of the container
respectively - means, the sum of diameters of the three tennis balls is equal to height of the cylindrical container

a tennis ball is a sphere and the volume of a sphere is ; so, if the volume of a tennis ball is ,then

........this is radius and we need diameter:

now we know that the height of the cylindrical container is and we know the radius (which is equal to a radius of the tennis ball) is

the volume of the container is:

Answer by mananth(12270)   (Show Source):
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V ball = 240
V = 4/3 * pi * r^3
240 = 4/3 * pi * r^3
(240*3)/(4 * pi) = r^3
r^3=57.29
r=3.85 cm radius of the ball
diameter = 7.70cm
Since the balls are touching each other and 3 balls can be place in the cylinder
the height of cylinder = 3 * diameter
=>23.10cm
radius of cylinder = radius of ball
So cylinder volume = pi * r^2*h
r=3.85, h=23.10
substitute to get the answer
1075 cm^3 ( rounded off)

Question 744762: a solid glass sphere is cast with a radius of 30 cm. what is the volume to the nearest whole number of this sphere?

Answer by Alan3354(30993)   (Show Source):
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a solid glass sphere is cast with a radius of 30 cm. what is the volume to the nearest whole number of this sphere?
------------

Question 744678:

how many cubes 6in on an edge will fit into a bin that is 24in on an edge?
Answer by checkley79(3050)   (Show Source):
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EACH 6IN. CUBE IS 6^3=216 IN^3
THE BIN IS 24^3=13,824 IN^2
13,824/216=64 6 IN. CUBES WILL FIT IN THE BIN

Question 744461: The volume of a right tiangular prism is 600 cubic units. Find its volume if its dimensions are increased 2.5 times.
A. 9375
B. 3750
C. 1500
D. 600
Found 2 solutions by sachi, Alan3354:
Answer by sachi(392)   (Show Source):
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the changed volume=600*2.5*2.5*2.5=9375 units

Answer by Alan3354(30993)   (Show Source):
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The volume of a right tiangular prism is 600 cubic units. Find its volume if its dimensions are increased 2.5 times.
A. 9375
B. 3750
C. 1500
D. 600
--------------
=

Question 744443: A cylinder is 6 inches in diameter and 10 inches in height. It needs to be transferred into a rectangle and it has to have the same height and volume. Can you please help me?
Answer by rothauserc(206)   (Show Source):
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The problem states
A cylinder is 6 inches in diameter and 10 inches in height. It needs to be transferred into a rectangle and it has to have the same height and volume.
volume of cylinder is pi*r^2*h
volume of rectangular l*w*h
volume of cylinder is 22/7 * 9 * 10 = 282.9 cubic inches
so we have for the rectangular solid
282.9 = l*w*10
28.3 = l*w
then you can pick any l and w whose product is 28.3

Question 744357: A box is 12 centimeters wide, 18 centimeters long,and 6 centimeters deep what is the volume?
Answer by checkley79(3050)   (Show Source):
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V=LHW
V=12*18*6
V=1,296 CM^3.