Multiple choice

Find the volume of a frustum cone, whose base and upper area of a circle is 20 and 80 $m^2$. The height of the cone is 45.5 m.

  1. 6,270 $m^3$
  2. 6,170 $m^3$
  3. 2,123.33 $m^3$
  4. 6,470 $m^3$
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C Correct answer
Explanation

The volume of a frustum is V = (1/3) * h * (A1 + A2 + sqrt(A1 * A2)). Given A1 = 20, A2 = 80, and h = 45.5: V = (1/3) * 45.5 * (20 + 80 + sqrt(20 * 80)) = (1/3) * 45.5 * (100 + 40) = (1/3) * 45.5 * 140 = 2123.33.

AI explanation

Using the frustum volume formula V = (1/3) * h * (A1 + A2 + square root of (A1*A2)), substitute the base area A1 = 20, the upper area A2 = 80, and the height h = 45.5. The square root of 1600 is 40, making the sum of the areas 20 + 80 + 40 = 140. Multiply the values to get (1/3) * 45.5 * 140 = 6370 / 3 = 2,123.33 m^3.

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