Multiple choice

From a solid right circular cylinder with height 4 cm and radius of the base 3 cm, a right circular cone of the same height and the same radius is drilled out. Find the volume of the remaining solid.

  1. $55.42$ $cm^3$
  2. $65.42$ $cm^3$
  3. $75.42$ $cm^3$
  4. $85.42$ $cm^3$
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C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 3^2 * 4 = 36pi. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 3^2 * 4 = 12pi. Remaining volume = 36pi - 12pi = 24pi. 24 * 3.14159 = 75.398, which is approximately 75.42.

AI explanation

The volume of the remaining solid is found by subtracting the volume of the cone from the volume of the cylinder. Using the volume of a cylinder formula (pi * r^2 * h) gives pi * 3^2 * 4 = 113.14 cubic cm. Using the volume of a cone formula (1/3 * pi * r^2 * h) gives (1/3) * pi * 3^2 * 4 = 37.71 cubic cm. The difference is 113.14 - 37.71 = 75.42 cubic cm.

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