Multiple choice

There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. The ratio of their radii is

  1. $4: 1$
  2. $4: 3$
  3. $3:4$
  4. $1:4$
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A Correct answer
Explanation

Curved surface area S = pi*r*l. Given S1 = 2*S2 and l2 = 2*l1. So pi*r1*l1 = 2 * (pi*r2*l2). Substitute l2: pi*r1*l1 = 2 * pi * r2 * (2*l1). r1 = 4*r2. Thus r1/r2 = 4/1.

AI explanation

Let the curved surface areas be πr1l1 for the first cone and πr2l2 for the second. From the given information, πr1l1 = 2(πr2l2) and l2 = 2l1. Substituting the second equation into the first yields πr1l1 = 2(πr2 * 2l1), which simplifies to r1 = 4r2. Therefore, the ratio of their radii (r1 : r2) is 4:1.

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