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.

9 : 32

Height of two Circular cones, H1:H2 :: 1:2 

⇒ H1 = 0.5 H2

Circumference of bases of the cones, C1:C2 :: 3:4 that is 2Πr1: 2Πr2 :: 3:4

⇒ r1:r2 = 3:4

⇒ r1 = 3/4 r2

Volumes, V1:V2 :: 1/3(Π H1 \( {r1}^{2} \) : 1/3(Π H2 \( {r2}^{2} \)

V1:V2 :: 9/16 × 0.5 : 1

V1:V2 :: 9/32 : 1 :: 9:32

The correct answer is Option (2) → 9 : 32