Multiple choice

The base and top radius of a truncated cone is 20 mm and 10 mm respectively. The height of the cone is 360 mm. What is the volume of a truncated cone? (Use $\pi$ = 3).

  1. 252,000 mm$^3$
  2. 242,000 mm$^3$
  3. 232,000 mm$^3$
  4. 222,000 mm$^3$
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A Correct answer
Explanation

The volume of a truncated cone is V = (1/3) * pi * h * (R^2 + r^2 + R*r). Using R=20, r=10, h=360, and pi=3: V = (1/3) * 3 * 360 * (20^2 + 10^2 + 20*10) = 360 * (400 + 100 + 200) = 360 * 700 = 252,000.

AI explanation

The volume of a truncated cone, or frustum, is found using the formula V = (1/3) * pi * (R^2 + R*r + r^2) * h, where R and r are the bottom and top radii, and h is the height. Plugging in the given values of R = 20, r = 10, h = 360, and pi = 3 gives V = (1/3) * 3 * (20^2 + 20*10 + 10^2) * 360. This simplifies to (400 + 200 + 100) * 360 = 700 * 360 = 252,000. The volume of the truncated cone is 252,000 cubic mm.

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