Multiple choice

From a solid cylinder whose height is 8 cm and radius is 6 cm a conical cavity of height 8 cm and base radius 6 cm is hollowed out Find the volume of the remaining solid

  1. $\displaystyle 603cm^{3}$
  2. $\displaystyle 720cm^{3}$
  3. $\displaystyle 548cm^{3}$
  4. $\displaystyle 637cm^{3}$
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A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 6^2 * 8 = 288 * pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 6^2 * 8 = 96 * pi. Remaining volume = 288 * pi - 96 * pi = 192 * pi. Using pi approx 3.14159, 192 * 3.14159 = 603.18, which rounds to 603.

AI explanation

To find the remaining volume, subtract the volume of the cone from the volume of the cylinder. Using pi as 22/7, the cylinder volume is (22/7)6*6*8 = 905.14 cubic cm, and the conical cavity volume is (1/3)(22/7)*6*6*8 = 301.71 cubic cm. The difference is 905.14 minus 301.71, which is 603.43 cubic cm, matching the approximation. The result is 603 cubic cm.

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