Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Show that their volumes are in the ratio 3:1.

Question

Philoid · Accepted Answer

Given,

Ratio of the heights = h₁ : h₂ = 1:3

Let the heights of the cones be x and 3x,

Ratio of radius of base of the two cones = r₁:r₂ = 3:1

So,

Let the radius be 3x and x for the cones and volume will be v₁ and v₂

So, ratio of the volume of the two cones will be 3:1