Multiple choice

The volume of a right circular cone is equal to the volume of a right circular cylinder. The height and the radius of the cylinder are 9 cm and 20 cm respectively. If the height of the cone is 108 cm, then the radius, in cm, is- लम्ब वृत्ताकार शंकु का आयतन लम्ब वृत्ताकार सिलेंडर के आयतन के बराबर है। सिलेंडर की ऊँचाई और त्रिज्या क्रमशः 9 सेमी. और 20 सेमी. है। यदि शंकु की ऊँचाई 108 सेमी. है, तो उसकी त्रिज्या कितनी (सेमी. में) होगी?

  1. 12

  2. 20

  3. 10

  4. 14
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C Correct answer
Explanation

Volume of cylinder = πr²h = π × 20² × 9 = 3600π cubic cm. Volume of cone = (1/3)πr²h = (1/3) × π × r² × 108 = 36πr². Setting volumes equal: 36πr² = 3600π, which gives r² = 100, so r = 10 cm. The cone has a smaller radius but greater height to achieve the same volume.

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