Question

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

(a) 1 : 2

(b) 2 : 1

(c) 4 : 1

(d) $\sqrt{2}$ : 1

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 find 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 cone to the height of the hemisphere =

Here, Volume of the hemisphere = volume of the cone

Therefore, the ratio of the heights of the cone and the hemisphere is. So, the correct option is (b)