Question

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

Options

• 1 : 2

•  2 : 1

• 4 : 1

• \[\sqrt{2}\] : 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 = `h/x`

Here, Volume of the hemisphere = volume of the cone

`(2/3) pi r_h^3 = (1/3) pi r_c ^2 h `

`(2/3) pi (x)^3 = (1/3) pi (x)^2 h`

`(2/3) (x) = (1/3) h`

         `2x = 1h`

       `h/x = 2/1`

Therefore, the ratio of the heights of the cone and the hemisphere is 2 : 1.