Question

The curved surface area of a solid sphere is equal to the surface area of a solid right circular cylinder. The lengths of both height and diameter of cylinder are 12 cm . Find the length of radius of the sphere.

Answer 1

Let the radius of the sphere be r cm.
`therefore` curved surface area of the solid sphere =`4pir^(2)` sq-cm
The radius of the right circular cylinder`=(12)/(2)cm=6cm.` and heght of it =12 cm.
`therefore` surface area of the right circular cylinder =`2pixx6xx12` sq-cm.
As per question, `4pir^(2)=2pixx6xx12 or, r^(2)`=36 or , r=6
Hence the required radius of the sphere=6cm.