Multiple choice

A vessel is in the form of a frustum of a cone. Its radius at top end is 8 cm and the bottom end is 12 cm. Its height is 21 cm. Find the volume of the frustum cone.

  1. 1,128 $\pi {cm}^3$
  2. 3,128 $\pi {cm}^3$
  3. 4,128 $\pi {cm}^3$
  4. 2,128 $\pi {cm}^3$
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D Correct answer
Explanation

Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). Here R=12, r=8, h=21. Volume = (1/3) * pi * 21 * (144 + 64 + 96) = 7 * pi * 304 = 2128 * pi.

AI explanation

The volume of a frustum of a cone is calculated using the formula (1/3) * pi * h * (R^2 + r^2 + Rr). Substituting the given height and radii gives (1/3) * pi * 21 * ((12)^2 + (8)^2 + 12 * 8). Simplifying the expression inside the brackets gives 144 + 64 + 96, which equals 304. The final volume is 7 * pi * 304, resulting in 2128 * pi cubic centimeters. The volume of the frustum cone is 2,128 pi cm^3.

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