What is the volume of a sphere with a surface area of 25pi

(125/6)π units³

Step-by-step explanation:

The formula for the surface area of a sphere is A = 4πr².  Solving this for r² yields:

                     A

            r² =

                     4π

and in this case r² is:

                    25π

            r² = , or 25/4 units²

                     4π

Thus, the radius, r, is 5/2 units.

The volume of a sphere of radius r is V = (4/3)πr³ units³

Here, that volume is V = (4/3)π(5/2)³ units³

                                         4π     125 units³

                                   =   · = (125/6)π units³

                                           3            8