Question

The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?

Answer 1

Let the radius of the first cone = 2x

And height of the first cone = h₁

Then,

Volume of the first cone `=1/3 pir^2 h                 `

                                        `=1/3 pi(2x) ^2 h_1 `       ............. (1)

The radius of the second cone = x

Height of the second cone = h₂

Then,

Volume of the second cone `=1/3 pir^2 h                 `

                                             `=1/3 pi(x) ^2 h_2 ` 

Since,

The volumes of the two cones are equal.

Or `h_1 :h_2 = 1 : 4`