Question

The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and the radius of the smaller base is r₂ units. If h₂ : h₁ = 1 : 2 then r₂ : r₁ is

Options

• 1 : 3

• 1 : 2

• 2 : 1

• 3 : 1

Answer 1

1 : 2

Explanation;

Hint:

h₂ : h₁ = 1 : 2

h₁ : h₂ = 2 : 1

Ratio of their volumes

= `1/3 pi"h"_1 ("r"_1^2 + "r"_2^2 + "r"_1"r"_2) : 1/3pi"h"_2 ("r"_1^2 + "r"_2^2 + "r"_1"r"_2)`

= 2(r₁² + r₂² + r₁r₂) : 1 (r₁² + r₂² + r₁r₂)

Volume is 2 : 1 the ratio of their radius also 2 : 1

r₁ : r₂ = 2 : 1 But r₂ : r₁ = 1 : 2