## Volume

There are different formulas for measuring volumes of different
vessels or containers. For a cuboid the formula is length × width ×
height. This can be generalized for all volumes by multiplying the
surface area of the base with the thickness or height, assuming the
height of the object is of a uniform shape (i.e. a cylinder or
rectangular prism).

When looking at varying values for length, breadth or height,
you must separate the varying parts of the unit whose volume you
wish to measure.

For example: a pool which has a shallow end and a deep end. To
obtain the volume of the entire pool, you would have to calculate
two volumes (one for the shallow end, with a small height, and one
for the deep end, with a large height.) then add the two answers to
obtain complete volume. Or, you could average the height for the
entire pool based on average height as a ratio in terms of length.
using that as a value of height, you could then forgo such issues
of varying values.

Another method of measuring volume, especially with irregularly
shaped objects is using "displacement." Fill a cubic container
large enough in which to fit the object to be measured with water,
measuring the height of the water line and calculating the volume.
Sink the object under the water and take the water line measurement
again.

The second measurement of volume minus the first measurement
gives the volume of the object, assuming that the object is
enclosed and non-absorbent.

### Specific
Formulas

**Annulus** = pi × (outer radius2 - inner radius2)

**Trapezoid** = (bottom base + top base) ÷ (2 × height)

**Triangle** = (base × height) ÷ 2

**Cube** = length × width × height

**Sphere** = (4/3) × pi × radius3

**Cylinder** = pi × radius2 × height

**Cone** = pi × radius2 × length ÷ 3

**Torus** (donut) = 2 × pi2 × (radius of cross-sectional
circle center)2 × (torus radius (center to circle middle))

- Or if you want to measure water 1 gram = 1 milliliter = 1
centimeter3

- As an integral in calculus, the volume is the area of a thin
slice integrated in a direction perpendicular to the face of the
slice. The area must be expressed as a function of the position of
the thin slice.

*Note*: length and width is the same as:

base × height

length × height

width × height