Multiple choice

The volume of a frustum cone is 1,600 $mm^3$, whose base and upper area of a circle is 16 and 100 $mm^2$. Find the height of the cone.

  1. 30.76 mm

  2. 11.25 mm

  3. 12.25 mm

  4. 13.25 mm
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A Correct answer
Explanation

The volume of a frustum is V = (h/3) * (A1 + A2 + sqrt(A1 * A2)). Given V = 1600, A1 = 16, and A2 = 100, we have 1600 = (h/3) * (16 + 100 + sqrt(1600)). This simplifies to 1600 = (h/3) * (116 + 40) = (h/3) * 156. Thus, 1600 = 52h, so h = 1600/52 = 30.769 mm.

AI explanation

Using the frustum volume formula V = (1/3) * h * (A1 + A2 + square root of (A1*A2)), substitute the volume V = 1600, the base area A1 = 16, and the upper area A2 = 100. The square root of 1600 is 40, making the sum of the areas 16 + 100 + 40 = 156. Rearrange the formula to solve for height as h = (3 * V) / 156 = 4800 / 156 = 30.76 mm.

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