Question

Two-cylinder have bases of the same size. The diameter of each is 14 cm. One of the cones is 10 cm high and the other is 20 cm high. Find the ratio between their volumes.

Answer 1

	Cone I	Cone II
Base diameter	14 cm	14 cm
Base radius	r1 = 7 cm	r2 = 7 cm
Height	h1 = 10 cm	h2 = 20 cm
Volume	V1 = π r12h1	V2 = πr22h2

Volume = V₁ = π r₁²h₁ : V₂= πr₂²h₂

Volume = π x (7)² x 10 cm³ : π x (7)² x 20 cm³

Volume = 490 π cm³ : 980 π cm³

∴ `V_1/V_2 = (490 π)/(980 π) = 1/2`

∴ V₁ : V₂ = 1 : 2.