Multiple choice

From a circular cylinder of diameter $10 cm$ and height $12 cm$, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid. Leave the answer in $\pi$.

  1. $210\pi $ $cm^3$
  2. $660\pi $ $cm^3$
  3. $220\pi $ $cm^3$
  4. $200\pi $ $cm^3$
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D Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 5^2 * 12 = 300pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 5^2 * 12 = 100pi. Remaining volume = 300pi - 100pi = 200pi.

AI explanation

The volume of a cylinder is pi*r^2*h, so with a radius of 5 cm and height of 12 cm, the cylinder volume is pi * 5^2 * 12 = 300*pi cubic cm. The volume of the conical cavity is (1/3)*pi*r^2*h, which evaluates to (1/3) * pi * 5^2 * 12 = 100*pi cubic cm. Subtracting the cone's volume from the cylinder's volume leaves 300*pi - 100*pi = 200*pi cubic cm.

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