Multiple choice

If the radius and slant height of a cone are $20 \ cm$ and $29 \ cm$ respectively. Find its volume.

  1. $8800 \ {cm}^{3}$
  2. $800 \ {cm}^{3}$
  3. $880 \ {cm}^{3}$

  4. None of these
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A Correct answer
Explanation

Radius r = 20, slant height l = 29. Height h = sqrt(l^2 - r^2) = sqrt(29^2 - 20^2) = sqrt(841 - 400) = sqrt(441) = 21. Volume = (1/3) * pi * r^2 * h = (1/3) * (22/7) * 20^2 * 21 = 22 * 400 = 8800.

AI explanation

First, we must find the height of the cone using the Pythagorean theorem, since l^2 = r^2 + h^2. Substituting the slant height of 29 cm and radius of 20 cm, we have 29^2 = 20^2 + h^2, which gives 841 = 400 + h^2, meaning the height is 21 cm. Using the cone volume formula V = (1/3) * pi * r^2 * h, the volume is (1/3) * (22/7) * 20 * 20 * 21, resulting in 8800 cubic cm.

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