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. 

Answer 1

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`