Multiple choice

From a right circular cylinder with height $10\ cm$ and radius of base $6\ cm$, a right circular cone of the same height and base is removed. Find the volume of the remaining solid

  1. $754.28\ {cm}^{3}$
  2. $714.17\ {cm}^{3}$
  3. $654.18\ {cm}^{3}$
  4. $754.82\ {cm}^{3}$
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A Correct answer
Explanation

Volume of cylinder = pi*r^2*h = pi*36*10 = 360*pi. Volume of cone = (1/3)*pi*r^2*h = 120*pi. Remaining volume = 240*pi. Using pi = 3.14159, 240*pi is approx 753.98, which is closest to 754.28.

AI explanation

The volume of the remaining solid is the difference between the volume of the cylinder and the volume of the removed cone, as both share the same base and height. The cylinder volume is pi times six squared times ten, which equals 360 pi. The cone volume is one third times pi times six squared times ten, which equals 120 pi. Subtracting the two gives a remaining volume of 240 pi, and using twenty-two sevenths for pi results in approximately 754.28 cubic cm.

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