Question

The ratio of radii of two cylinders is 1 : 2 and heights are in the ratio 2 : 3. The ratio of their volumes is ______.

Options

• 1 : 6

• 1 : 9

• 1 : 3

• 2 : 9

Answer 1

The ratio of radii of two cylinders is 1 : 2 and heights are in the ratio 2 : 3. The ratio of their volumes is 1 : 6

Explanation:

Let r₁, r₂ be radii of two cylinders and h₁, h₂ be their heights.

Then `r_1/r_2 = 1/2` and `h_1/h_2 = 2/3`

Now, `V_1/V_2 = (pir_1^2 h_1)/(pir_2^2 h_2)`

= `(r_1/r_2)^2 xx h_1/h_2`

= `(1/2)^2 xx 2/3`

= `1/4 xx 2/3`

= `1/6`

= 1 : 6

Hence, V₁ : V₂ = 1 : 6