The diameter and height of a right circular cylinder are equal to the diameter of a sphere. Find the ratio of volumes of cylinder and sphere.

Explanation

Let radius of sphere = r
`therefore` Volume of sphere `V_(1)=(4)/(3)pi r^(3)`
Now, the diameter of cylinder = diameter of sphere = 2r
`therefore` radius of cylinder = r and height of cylinder = 2r
Now, volume of cylinder `= pi r^(2)(2r)=2pi r^(3)`
`therefore ("Volume of cylinder")/("Volume of sphere")=(2pi r^(3))/((4)/(3)pi r^(3))=(3)/(2)`
`rArr` Required ratio = 3 : 2