(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}
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 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}).
