Multiple choice

The height of the frustum cone is $18$ in. The area of the top and bottom circle of the cone is $4$ in$^2$ and $16$ in$^2$ respectively. Find its volume.

  1. $168$ in$^3$
  2. $158$ in$^3$
  3. $146$ in$^3$
  4. $148$ in$^3$
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A Correct answer
Explanation

Volume of a frustum = (1/3)pi*h(R^2 + r^2 + R*r). Here, pi*R^2 = 16 and pi*r^2 = 4. So R^2 = 16/pi and r^2 = 4/pi. R = 4/sqrt(pi), r = 2/sqrt(pi). Volume = (1/3)h(Area1 + Area2 + sqrt(Area1*Area2)). Volume = (1/3)18(16 + 4 + sqrt(16*4)) = 6*(20 + 8) = 6*28 = 168.

AI explanation

Using the formula for the volume of a frustum, which is one third of the height multiplied by the sum of the top area, the bottom area, and the square root of their product, we substitute the given values. This yields one third of 18 times the quantity (4 plus 16 plus the square root of 4 times 16). The square root of 64 is 8, making the sum inside the parentheses equal to 28. Multiplying these values results in a volume of 168 cubic inches.

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