Question

Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. Then the ratio of their volumes is ………

A) 3 : 1 

B) 1 : 4 

C) 1 : 3 

D) 1 : 9

Answer 1

Correct option is: A) 3 : 1

Given that \(\frac {h_1}{h_2} = \frac 13\) & \(\frac {r_1}{r_2} = \frac 31\)

\(\therefore\) \(\frac {V_1}{V_2} \) = \(\frac {\frac 13 \pi r^2_1\, h_1}{\frac 13 \pi r^2_2\, h_2}\) = \((\frac {r_1}{r_2})^2 (\frac {h_1}{h_2}) = (\frac 31)^2 \times \frac 13 = \frac 93 = \frac 31 = 3 :1\)

Hence, the ratio of their volume is 3 : 1.

Answer 2

Correct option is: A) 3 : 1