The heights of two right circular cones are in the ratio 1 : 2 and the circumferences of their bases are in the ratio 3 : 4. Find the ratio of their volumes.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9 : 32
The circumference \(2\pi r\) is proportional to the radius, so the radii are in the same ratio as the circumferences, 3 : 4. The volume of a cone, \(\displaystyle\frac{1}{3}\pi r^2h\), is proportional to \(r^2h\).
\(r_1:r_2=3:4\) and \(h_1:h_2=1:2\)
\(V_1:V_2=r_1^2h_1:r_2^2h_2=(9\times1):(16\times2)=9:32\)