Question

The numerical value of the volume of a sphere is equal to the numerical value of its surface area.

Find the exact value of the radius of this sphere.​

Answer 1

The radius of this sphere is
`3`.

Explanation:

The volume of a sphere of radius
`r` is:

`\displaystyle V = (4)/(3)\, \pi\, r^(3)`.

The surface area of a sphere of radius
`r` is:

`A = \pi\, (2\, r)^(2)`.

Equate the right-hand side of these two expressions and solve for
`r`:

`r = 3`.

In other words, the radius of this sphere is
`3`.