Volume Formulas

Note: “ab” means “a” multiplied by “b”. “a2” means “a squared”, which is the same as “a” times “a”. “b3” means “b cubed”, which is the same as “b” times “b” times “b”.

Be careful!! Units count. Use the same units for all measurements. Examples

cube = a 3 

rectangular prism = a b c 

irregular prism = b h 

cylinder = b h = pi r 2 h 

pyramid = (1/3) b h 

cone = (1/3) b h = 1/3 pi r 2 h 

sphere = (4/3) pi r 3 

ellipsoid = (4/3) pi r1 r2 r3 

 

 Units

Volume is measured in “cubic” units. The volume of a figure is the number of cubes required to fill it completely, like blocks in a box.

Volume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed.

If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches. (Cubic inches can also be written in3.)

Be sure to use the same units for all measurements. You cannot multiply feet times inches times yards, it doesn’t make a perfectly cubed measurement.

The volume of a rectangular prism is the length on the side times the width times the height. If the width is 4 inches, the length is 1 foot and the height is 3 feet, what is the volume?

NOT CORRECT …. 4 times 1 times 3 = 12

CORRECT…. 4 inches is the same as 1/3 feet. Volume is 1/3 feet times 1 foot times 3 feet = 1 cubic foot (or 1 cu. ft., or 1 ft3).