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 3dimensional shapes, including rectangular prisms, cylinders and spheres.
Calculating Volume
Rectangular Prisms
A rectangular prism is a solid, 3dimensional 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
Cylinders
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
Spheres
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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