Question

A sphere has a volume and surface area which have equal numerical values. Calculate the radius of the sphere for which this is true. Verify that your answer is correct by then calculating both the volume and surface area.

Answer 1

The formula for the volume of a sphere is:

`v = (4)/(3) \pi {r}^(3)`

The formula for the surface area of a sphere is:

`a = 4\pi {r}^(2)`

Since they have equal numerical values, we know that the two are equal and we can say:

`(4)/(3) \pi {r}^(3) = 4\pi {r}^(2)`

Solving for r, pi cancels out and we get:

`r = 3`

Now plug r = 3 into both of the formulas to make sure that they are equal (hint: they are)

Answer: r = 3