Correct Answer - Option 3 : 11 : 12
Given
Ratio of two cones volume = 99 : 48
Ratio of two cones radius = 3 : 2
Formula used
Volume of cone = (1/3)πr2h
Where r and h are radius and height of cone respectively
Calculation
[(1/3)πR2H]/[(1/3)πr2h] = 99/48
R, H, r and h are radius and height of first and Second cone
(3/2)2× (H/h) = 99/48
⇒ (9/4) × (H/h) = 99/48
⇒ H/h = (99 × 4)/(48 × 9)
⇒ H/h = 11/12
⇒ H : h = 11 : 12
∴ The ratio of the two cones height is 11 : 12.
