Multiple choice

The volume of frustum of a cone is 3,600 cm$^3$. The area of the bottom circle of the cone is 4 cm$^2$ and the area of the top circle of the cone is 16 cm$^2$. Find its height.

  1. 385.7 cm

  2. 375.7 cm

  3. 365.7 cm

  4. 355.7 cm
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A Correct answer
Explanation

Volume of frustum V = (1/3) * pi * h * (R^2 + r^2 + R*r). Given areas A1 = pi*R^2 = 16 and A2 = pi*r^2 = 4, so R = 4/sqrt(pi) and r = 2/sqrt(pi). Substituting these into the volume formula leads to h = 3600 / (1/3 * (16 + 4 + sqrt(16*4))) = 3600 / (1/3 * 28) = 385.7 cm.

AI explanation

The volume of a frustum is one third of the height multiplied by the sum of the top area, the bottom area, and the square root of their product. Substituting the known values gives 3600 equals one third of the height times the quantity (4 plus 16 plus the square root of 64). The sum inside the parentheses evaluates to 28. Solving for the height gives 3600 equals 28 over 3 times the height, which results in a height of approximately 385.7 centimeters.

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