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

Accepted Solution

Answer:(125/6)π units³Step-by-step explanation:The formula for the surface area of a sphere is A = 4πr².  Solving this for r² yields:                      A             r² = ------                      4πand in this case r² is:                     25π             r² = ---------, or 25/4 units²                      4πThus, the radius, r, is 5/2 units.The volume of a sphere of radius r is V = (4/3)πr³ units³Here, that volume is V = (4/3)π(5/2)³ units³                                          4π     125 units³                                    =   ------ · ------------------ = (125/6)π units³                                            3            8