If the volume of a sphere is equal to that of a cylinder having the same radius, then find the ratio of the radius to the height of the cylinder.

3 : 4

We know that,

The volume of a sphere = \(\frac{4}{3}\) × π × (radius)³

The volume of a cylinder = π × (radius)² × (height)

Radius of sphere = radius of cylinder = r

Also, the height of the cylinder = h

So, \(\frac{4}{3}\) × π × r³ = π × r² × h

= \(\frac{4}{3}\) × r = h

= \(\frac{r}{h}\) = \(\frac{3}{4}\)