Multiple choice

The volume of frustum of a cone is 180.27 ft$^3$. The area of the bottom circle of the cone is 27 ft$^2$ and the area of the top circle of the cone is 12 ft$^2$. Find its height.

  1. 9.28 ft

  2. 9.38 ft

  3. 9.58 ft

  4. 9.48 ft
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D Correct answer
Explanation

The volume of a frustum of a cone is given by V = (1/3) * h * (A1 + A2 + sqrt(A1 * A2)), where A1 and A2 are the areas of the base and top circles. Substituting the given values, we get 180.27 = (1/3) * h * (27 + 12 + sqrt(27 * 12)) = 19 * h. Solving for h gives h = 180.27 / 19 = 9.48 ft.

AI explanation

The volume of a frustum is given by V equals one third multiplied by pi multiplied by height times the sum of the base area, the top area, and the square root of the product of the base and top areas. The radii are the square roots of 27 divided by pi and 12 divided by pi, so the square root of their product equals the square root of 324 divided by pi squared, which simplifies to 18 divided by pi. Substituting the volume of 180.27 gives 180.27 equals one third multiplied by pi multiplied by height times (27 plus 12 plus 18 divided by pi), which simplifies to height equals 540.81 divided by 143.14. Therefore, the height is approximately 9.48 feet.

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