Multiple choice

Find the volume of the frustum cone whose base and top radius is 21 in and 5 in respectively. The height of the cone is 300 in. (Use $\pi$ = 3).

  1. 181,300 in$^3$
  2. 171,300 in$^3$
  3. 161,300 in$^3$
  4. 151,300 in$^3$
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B Correct answer
Explanation

Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). With R=21, r=5, h=300, and pi=3: V = (1/3) * 3 * 300 * (21^2 + 5^2 + 21*5) = 300 * (441 + 25 + 105) = 300 * 571 = 171,300 in^3.

AI explanation

Using the frustum volume formula V = (1/3) * pi * h * (R^2 + r^2 + R*r), substitute R = 21, r = 5, h = 300, and pi = 3. Calculate the radii components as 21^2 = 441, 5^2 = 25, and 21 * 5 = 105, which sum to 571. Multiply the values to get (1/3) * 3 * 300 * 571 = 300 * 571 = 171,300 in^3.

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