Question

A cone of base radius 4 cm is divided into two parts by drawing a plane through the midpoint of its height and parallel to its. Compare the volume of the two parts.

Answer 1

ΔABC ∼ ΔAPQ

∴ `h/(2h) = r_1/4`

⇒ r₁ = 2 cm

Volume of smaller cone = `1/3 πr_1^2h`

= `1/3 π(2)^2h`

= `1/3 xx 4πh`

Volume of frustum = `1/3 πh(r_1^2 + r_2^2 + r_1r_2)`

= `1/3 π xx h(2^2 + 4^2 + 2 xx 4)`

= `1/3 πh xx 28`

∴ Required ratio = `(1/3 xx 4πh)/(1/3 xx 28 πh)`

= `4/28`

= `1/7`