Sum of volume of cone and volume of cylinder is (15840) cm(^{3}) and height of both cone and cylinder is same i.e. (20) cm. If radius of cylinder is (12) cm then find the ratio of radius of cone to radius of cylinder.
A
Correct answer
Explanation
Cylinder volume = π × 12² × 20 = 1440π cm³. Total volume = 15840 cm³. Cone volume = 15840 - 1440π. Using π ≈ 22/7: 1440π = 1440 × 22/7 = 31680/7 ≈ 4525.7. Cone volume ≈ 15840 - 4525.7 = 11314.3 cm³. Cone volume = (1/3) × π × r² × 20, so r² = (3 × 11314.3)/(20π) ≈ 33942.9/(20 × 22/7) ≈ 33942.9/62.86 ≈ 540. So r ≈ 18 cm. Ratio r_cone : r_cylinder = 18 : 12 = 3 : 2. Option A is correct.