Question

A sphere and a cube has same surface area.Show that the ratio of the volume of sphere to cube is `sqrt6:sqrtpi`

Answer 1

Let the radius of sphere be r and the side of cube be x. Then
`4pi r^(2)=6x^(2)`
`rArr (r^(2))/(x^(2))=(6)/(4pi)`
`therefore (V_(s))/(V_(c ))=((4)/(3)pi r^(3))/(x^(3))=(4)/(3)pi (r^(2))/(x^(2)),(r )/(x)`
`=(4pi)/(3)xx(6)/(4pi)sqrt((6)/(4pi))`
`= sqrt((6)/(4pi)xx2xx2)=sqrt(6):sqrt(x)`