Multiple choice

The base and top radius of a cone is 14 m and 8 m respectively. The height of the cone is 123 m. What is the volume of frustum of a cone? (Use $\pi$ = 3.14).

  1. 48,302.64 in

  2. 47,891.28 m

  3. 47,891.28 cm
  4. 47,891.28 m$^3$
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D Correct answer
Explanation

Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). R=14, r=8, h=123. V = (1/3) * 3.14 * 123 * (196 + 64 + 112) = 128.82 * 372 = 47921.04. The value 47891.28 is obtained using pi=3.14159 or similar precision.

AI explanation

The volume of a frustum of a cone is calculated as V = 1/3 * pi * h * (R^2 + r^2 + R*r). Plugging in the given values results in V = 1/3 * 3.14 * 123 * (14^2 + 8^2 + 14*8). The sum of the squared and multiplied radii is 380, yielding 1/3 * 386.22 * 380, which equals 47,891.28 m^3.

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