Multiple choice

The height of the frustum cone is 30 cm. The area of the top and bottom circle of the cone is 6 cm$^2$ and 96 cm$^2$ respectively. Find its volume.

  1. 1,260 cm$^3$
  2. 1,700 m$^3$
  3. 1,260 m$^3$

  4. 1,260 cm
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A Correct answer
Explanation

Volume of frustum = (1/3)h(A1 + A2 + sqrt(A1*A2)). h = 30, A1 = 6, A2 = 96. V = (1/3)30(6 + 96 + sqrt(6*96)) = 10*(102 + sqrt(576)) = 10*(102 + 24) = 10*126 = 1260 cm^3.

AI explanation

Using the formula for the volume of a frustum, which is one third times the height times the sum of the top area, bottom area, and the square root of their product, we substitute the given values. This gives one third of 30 times the quantity (6 plus 96 plus the square root of 6 times 96). The square root of 576 is 24, so the values inside the parentheses sum to 126. Multiplying one third of 30 by 126 gives a total volume of 1260 cubic centimeters.

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