Question

A sphere of maximum volume is cut out from a solid hemisphere of radius 6cm. What is the volume of the cut out sphere?

Answer 1

A sphere with maximum volume that cna be cut out from a solid hemisphere will be the one whose diameter will be equal to that of the radius of the hemisphere.

i.e. the radius of the sphere = 1/2 radius of hemisphere = 3 cm
Hence, its volume = 4/3 *pi*r3
Volume = 4/3 *pi*33
Volume = 792/7 cm3 = 113.14 cm3
hope it helps