Hands-on math!


Volume is the measure of the amount of space inside of a solid (3-dimensional) figure, like a cube, sphere, cylinder or pyramid.
It's units are always "cubic" somethings, that is, the number of little element cubes that fit inside the figure.

The formula for the volume of a rectangular prism is:

Area = L x W x H


L = length

W = width

H = height

For example, the volume of a shoe box (a parallelepiped) that is 4 inches by 6 inches by 12 inches is 4 x 6 x 12 = 288 cubic inches. This means that it would take 288 little 1-inch cubes to fill the shoe box.

Here are the formulas for the volume of some common 3-D shapes:
Sphere V = 4 R3 / 3 where R is the radius of the sphere
Pyramid V = (L W H) / 3 where L = base length, W = base width, H = pyramid height
Cylinder V = L R2 where L is the length of the cylinder
and R is the radius of the end circle
Cone V = H R2 / 3 where H = the cone's height and R is the radius of the base