Multiple choice

The volume of the frustum of a cone is 4,200 mm$^3$. The bottom and top radius are R = 20 mm and r = 10 mm. Find its height. (Use $\pi$ = 3). Round off your answer to nearest whole number.

  1. 6 mm

  2. 7 mm

  3. 8 mm

  4. 10 mm
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A Correct answer
Explanation

Volume = (1/3) * pi * h * (R^2 + r^2 + R*r). 4200 = (1/3) * 3 * h * (20^2 + 10^2 + 20*10). 4200 = h * (400 + 100 + 200). 4200 = 700 * h. h = 6.

AI explanation

The volume of a frustum of a cone is calculated as V = 1/3 * pi * h * (R^2 + r^2 + R*r). Plugging in the given values results in 4,200 = 1/3 * 3 * h * (20^2 + 10^2 + 20*10). The sum of the radii terms is 700, so dividing 4,200 by 700 gives a height of 6 mm.

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