Multiple choice

From a right circular cylinder of radius 10 cm. and height 21 cm., a right circular cone of same base-radius is removed. If the volume of the remaining portion is 4400 cm3 then find the height of the removed cone. एक लम्ब वृत्तीय बेलन की त्रिज्या 10 सेमी. और ऊँचाई 21 सेमी. है। इनमें से एक लम्बवृत्तीय शंकु उसी त्रिज्या का काटा जाता है। यदि शेष भाग का आयतन 4400 सेमी3. हो तो काटे गये शंकु की ऊँचाई ज्ञात कीजिए।

  1. 14

  2. 21

  3. 18

  4. 16
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B Correct answer
Explanation

Cylinder volume = πr²h = π(100)(21) = 2100π ≈ 6600 cm³. Cone volume = (1/3)πr²h_cone = (100π/3)h. Remaining volume = 6600 - (100π/3)h = 4400. Solving: (100π/3)h = 2200, h = 2200 × 3/(100π) = 66/π ≈ 21. Height 14 would give remaining volume 5133, 18 gives 4800, 16 gives 5026.

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