Question

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Answer 1

In the given problem, we are given a cone and a hemisphere which have equal bases and have equal volumes. We need to show that the ratio of their heights.

So,

Let the radius of the cone and hemisphere be x cm.

Also, height of the hemisphere is equal to the radius of the hemisphere.

Now, let the height of the cone = h cm

So, the ratio of the height of hemisphere to the height of the cone =

Here, Volume of the hemisphere = volume of the cone

Therefore, the ratio of the heights is.