Multiple choice

The ratio of slant height and radius of a cone is $7:4$. If its curved surface area is $792\ {cm}^{2}$, then find its radius.

  1. $12\ cm$
  2. $21\ cm$
  3. $28\ cm$
  4. $33\ cm$
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A Correct answer
Explanation

Curved surface area of a cone is pi * r * l. Given l/r = 7/4, so l = 7r/4. Substituting into the formula: pi * r * (7r/4) = 792. Solving for r^2 gives r^2 = (792 * 4) / (pi * 7). Using pi = 22/7, r^2 = 144, so r = 12.

AI explanation

Let the slant height and radius of the cone be 7x and 4x respectively. Using the curved surface area formula, we write pi * r * l = 792, which becomes pi * 4x * 7x = 792. Substituting pi as 22/7 gives 22/7 * 28 * x^2 = 792, so 88 * x^2 = 792. We find x^2 = 9, meaning x = 3. Therefore, the radius is 4 * 3 = 12 cm.

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