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TIFR CSE 2010 | Part A | Question: 17

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Suppose there is a sphere with diameter at least $6$ inches. Through this sphere we drill a hole along a diameter. The part of the sphere lost in the process of drilling the hole looks like two caps joined to a cylinder, where the cylindrical part has length $6$ inches. It turns out that the volume of the remaining portion of the sphere does not depend on the diameter of the sphere. Using this fact, determine the volume of the remaining part.

  1. $24\pi$ cu. inches
  2. $36\pi$ cu. inches
  3. $27\pi$ cu. inches
  4. $32\pi$ cu. inches
  5. $35\pi$ cu. inches
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This is the Napkin ring problem.

The volume of the remaining part is

$V =\dfrac{\pi h^3}{6}$

For $h=6, V = 36\pi$
Hence, the answer is option $(2)$.

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