Multiple choice

If the ratio of the radii of the two cones is 2 : 3 and the ratio of their slant heights is 9 : 4, then the ratio of their curved surface area is

  1. 3 : 2

  2. 1 : 2

  3. 1 : 3

  4. 2 : 3
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A Correct answer
Explanation

Curved Surface Area (CSA) = pi * r * l. Ratio of CSA1/CSA2 = (r1 * l1) / (r2 * l2) = (r1/r2) * (l1/l2) = (2/3) * (9/4) = 18/12 = 3/2.

AI explanation

The curved surface area of a cone is found using the formula pi times radius times slant height. Because the constant pi appears in both areas, the ratio of their curved surface areas is simply the product of their individual radius and slant height ratios. Multiplying the radius ratio of 2 divided by 3 by the slant height ratio of 9 divided by 4 gives 18 divided by 12. Simplifying this fraction results in the ratio 3 : 2.

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