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
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
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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.
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