Multiple choice

The height of the frustum cone is 210 m. The area of the top and bottom circle of the cone is 10 m$^2$ and 250 m$^2$ respectively. Find its volume.

  1. 20,700 m$^3$
  2. 21,700 m$^3$
  3. 22,700 m$^3$
  4. 23,700 m$^3$
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B Correct answer
Explanation

Volume of frustum = (h/3) * (A1 + A2 + sqrt(A1*A2)). V = (210/3) * (10 + 250 + sqrt(2500)) = 70 * (260 + 50) = 70 * 310 = 21,700.

AI explanation

Using the frustum volume formula of one third times the height times the sum of the top area, bottom area, and the square root of their product, we substitute the known values. This gives one third of 210 times the quantity (10 plus 250 plus the square root of 10 times 250). The square root of 2500 is 50, so the sum in the parentheses becomes 310. Multiplying these values results in a volume of 21700 cubic meters.

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