**( pi = = 3.141592…)**

### Volume Formulas

### Note: “ab” means “a” multiplied by “b”. “a^{2}” means “a squared”, which is the same as “a” times “a”. “b^{3}” 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* r_{1} r_{2} r_{3}

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 in^{3}.)

**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 ft^{3}).

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