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
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