If the radii and volumes of a solid right circular cone and a solid sphere be equal, then what will be the ratio of the length of diameter of the sphere and the height of the cone ?

Explanation

Let the radii of the cone and the sphere be r unit and the height of the cone be x - unit .
` :.` the volume of the cone ` = 1/3 pir^(2)x` cubic - unit
and the volume of the sphere `= 4/3 prr^(3) ` cubic - unit
As per question , ` 4/3 pir^(3) = 1/3 pir^(2) x `
` rArr 4r = x rArr 2r = x/2 rArr (2r)/x = 1/2 `
` rArr 2r : x = 1 : 2`
Hence the required ratio is 1:2