Multiple choice

From a solid cylinder whose height is 4 cm and radius is 3 cm, a conical cavity of height 4 cm and base radius 3 cm is hollowed out. What is the volume of the remaining solid?

  1. $9\pi\:cm^3$
  2. $15\pi\:cm^3$
  3. $21\pi\:cm^3$
  4. $24\pi\:cm^3$
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D Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 3^2 * 4 = 36 * pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 3^2 * 4 = 12 * pi. Remaining volume = 36 * pi - 12 * pi = 24 * pi.

AI explanation

The volume of the remaining solid is found by subtracting the volume of the conical cavity from the volume of the cylinder. Using the volume formulas, the cylinder's volume is pi*3^2*4 = 36*pi cubic cm, and the cone's volume is (1/3)*pi*3^2*4 = 12*pi cubic cm. Subtracting the cone from the cylinder gives 36*pi - 12*pi = 24*pi cubic cm. The result is 24*pi cubic cm.

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