Multiple choice

Two right circular cones of equal curved surface areas have their slant heights in the ratio of $3 : 5$. Find the ratio of their radii.

  1. $5:3$
  2. $8:15$
  3. $9:15$

  4. None of these
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A Correct answer
Explanation

Curved surface area of a cone is pi*r*l. Since areas are equal, pi*r1*l1 = pi*r2*l2. Thus r1/r2 = l2/l1. Given l1/l2 = 3/5, then r1/r2 = 5/3.

AI explanation

The curved surface area of a cone equals pi times radius times slant height. Setting the areas equal for two cones gives radius one times slant height one equals radius two times slant height two, meaning the ratio of radii is the inverse of the ratio of slant heights. Therefore, the radii are in the ratio 5 to 3.

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