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
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