The length of radius of base of a solid right circular cone is equal to the length of radius of a solid sphere . If the volume of the sphere is 2 times the volume of the cone , then find the ratio of the height and radius of base of the cone .

Explanation

Let the radius of the base of the cone = r unit
` :. ` the radius of the sphere = r unit
Let the height of the cone = h unit
` :.` the volume of the cone ` = 1/2 pi r^(2) h` cubic - unit
and the volume of the sphere `= 4/3 pi r^(3)` cubic - unit
As per question , ` 2xx 1/3 pi r^(2) h = 4/3 pir^(3)`
` rArr h/r = 4/2 rArr h/r = 2/1 rArr h : r = 2 : 1 `
Hence the required ratio is 2:1