Multiple choice

Find the volume of the frustum cone whose base and top radius is 20 ft and 10 ft respectively. The height of the cone is 300 ft. (Use $\pi$ = 3).

  1. 200,000 ft$^3$
  2. 220,000 ft$^3$
  3. 210,000 ft$^3$
  4. 230,000 ft$^3$
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C Correct answer
Explanation

The volume of a frustum is (1/3) * pi * h * (R^2 + r^2 + R*r). Given R=20, r=10, h=300, and pi=3: Volume = (1/3) * 3 * 300 * (20^2 + 10^2 + 20*10) = 300 * (400 + 100 + 200) = 300 * 700 = 210,000 ft^3.

AI explanation

Using the frustum of a cone volume formula, V equals one-third times pi times h times the sum of r1 squared plus r2 squared plus r1 times r2. Substituting the values gives one-third times 3 times 300 times the sum of 20 squared plus 10 squared plus 20 times 10. This simplifies to 300 times 700, resulting in 210,000 ft^3.

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