What will be the ratio of the diameter of the sphere and the height of a cylinder when the volumes of the sphere and the right circular cylinder are equal , given that the radii of the sphere and the cylinder are equal ?

Explanation

Let the radii of the sphere and the cylinder be r unit and the height of the cylinder be h unit .
As per question , ` pir^(2) h = 4/3 pir^(3) rArr 3h = 4r rArr 2.2r = 3h `
` rArr (2r)/h = 3/2 rArr 2r : h = 3: 2 `
Hence the ratio of the diameter of the sphere and the height of the cylinder is 3:2