Volume Math Problems: Homework Help for Students

Need help finding the volume of an object? This article explains how to find the volume of many 3-dimensional shapes, including rectangular prisms, cylinders and spheres.

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Calculating Volume

Rectangular Prisms

A rectangular prism is a solid, 3-dimensional object with three sets of parallel sides that are perpendicular to one another. A pack of playing cards is an example of a rectangular prism and so is a paperback book.

To find the volume of this kind of object, use the formula V = l x w x h, where V is the volume, l is the length, w is the width and h is the height. For example, here's how you would find the volume of a rectangular prism with a length of four feet, a width of two feet and a height of ten feet:

V = l x w x h

V = 4 x 2 x 10

V = 80 cubic feet

Sometimes, you'll just be given the area of the rectangular prism's base and its height. Since a rectangle's length times its width equals its area, you can substitute this value into the volume formula, like this: V = b x h. In this case, b is the area of the base and h is the height. To find the volume of a rectangular prism with a height of five meters and a base that's ten square meters, you'd use the following calculations:

V = b x h

V = 10 x 5

V = 50 cubic meters


A cylinder has a circular base, and its sides are perpendicular to this base. A can of soup is an example of a cylinder. To find the volume of a cylindrical object when you know the area of its base, you can use the formula V = b x h.

If you aren't given the area of the cylinder's base, you can find it using the formula A = (pi) r^2. A represents the area, pi equals 3.14 and r^2 is the radius of the base squared. Substitute this formula into the volume formula, and you get V = (pi) r^2 (h). For a cylinder that's three inches tall and has a base with a radius of five inches, here's how you calculate volume:

V = (pi) r^2 (h)

V = (3.14) (5^2) (3)

V = (3.14) (25) (3)

V = 235.5 cubic inches


The formula for the volume of a sphere is V = 4/3 (pi) r^3. Here's an example featuring a sphere with a radius of two centimeters:

V = 4/3 (pi) r^3

V = 4/3 (3.14) (2^3)

V = 4/3 (3.14) (8)

V = 33.493 cubic centimeters

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