Question

Two cones have their heights in the ratio 4:3 and the radii of their bases in the ratio 1:2. Find the ratio of their volumes.

• A. 4:9
• B. 1:3
• C. 2:9
• D. 2:5

Answer 1

Answer:

B. 1:3

The volume of a cone is given by:
$V = \frac{1}{3}\pi r^2 h$

Ratio of heights (= 4 : 3)

Ratio of radii (= 1 : 2)

Ratio of volumes:

$V_1 : V_2 = r_1^2 h_1 : r_2^2 h_2$

Substitute the ratios:
$= (1^2 \times 4) : (2^2 \times 3)$
$= 4 : 12$
$= 1 : 3$
(1 : 3)