In order to solve problems which require application of the

volume and

surface area for spheres, it is necessary to

- know how to
simplify
and
solve
expressions involving squares and cubes

A typical problem involving the

volume or

surface area of a sphere gives us various information about the size of the

sphere - usually one or more values for the volume, surface area, radius, or diameter. You will then be asked to calculate the other missing values based on this given information.

We use r = 5 in the formulas for

volume and surface area.

Volume: V =

cubic inches

Surface area: S =

square inches

It is difficult to inspect these answers for reasonableness. Care must be taken in arithmetic when squaring and cubing the radius.

Notice also that both formulas involve use of 4

p . If we rewrite the formula for volume, we can get a relationship between

volume and surface area:

where S is the surface area. This is not often a helpful relationship, but we may refer to it when comparing

volume and surface area.

For example, suppose the

surface area of a sphere equals twice the numerical value of its volume. What is the sphere's radius?

r = 3/2 = 1.5