Question

The radii of the base of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?

Answer 1

Let r₁ and r₂ be the radii of the base of a cylinder and a cone.

The volume of cylinder`V_1 = pir_1^2 h_1`…… (i)

The volume of cone `V_2 = pir_2^2 h_2`…… (ii)

Dividing (i) by (ii), the, we get

`V_2/v_2 = (pir_1^2 h_1)/(1/3pir_2^2 h_2)`

`(= 3 xx (r_1/r_2)^2 xx (h_1/h_2))/(((r_1/r_2 = 3/4 , h_1 /h_2 = 2/3, "given")))`

`V_1/V_2= 3 xx (3/4)^2 xx 2/3`

`V_1/V_2 = 9/8`

`V_1 : V_2 = 9:8`