The ratio of the heights of a right circular cone and a right circular cylinder is 8 : 9 and the ratio of the radii of their bases is 3 : 4. If the volume of the cylinder is 132 cm3, then the volume (in cm³) of the cone is:
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 22.
Let heights be 8h (cone) and 9h (cylinder)
Let radii be 3r (cone) and 4r (cylinder)
π(4r)2(9h) = 132
⇒ π × 16r2 × 9h = 132
⇒ 144πr2h = 132
⇒ πr2h = 132/144 = 11/12
Cone volume = (1/3)π(3r)2(8h) = 24πr2h
= 24 × (11/12)
= 22 cm3