#### Question

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

#### Solution

Given that, let height →h say

Height of `1^(st)` cone = h

Height of `2^(nd)`cone = 3h

Let the ratio of radii be r

∴ Radius of `1^(st)` cone=3r

Radius of` 2 ^(nd)` cone = r

∴ ratio of volume =` V_1/V_2`

⇒ `V_1/V_2=(1/3pir_1^2h_1)/(1/3pir_2^2h_2)=(r_1^2h_1)/(r_2^2h_2)`

=`((3r)^2xxh)/(r^2xx3h)`

`=(9r^2h)/(3r^2h)`

= 3/1

⇒ `v_1/v^2=3/1`

Is there an error in this question or solution?

Solution Two Cones Have Their Heights in the Ratio 1 : 3 and the Radii of Their Bases in the Ratio 3 : 1. Find the Ratio of Their Volumes. Concept: Surface Area of a Right Circular Cone.