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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`
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