Question

If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?

Answer 1

Given that,

A cone and a sphere have equal radii and equal volume

i.e., volume of cone = volume of sphere

`1/3pi r_1^2 = 4/3 pir^3`

`r^2h = 4r^3`

`h = 4r^3`

`h = 4r`

`h = (2r) xx 2`

`h / 2r = 2/1`

`h/2 = 2/1` (diameterd = 2r)

`h : d = 2:1 or d: h = 1 : 2`