Question

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

Answer 1

There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. The ratio of their radii = 1/4

Given:

There are two cones.

The curved surface area of one is twice that of the other.

⇒ CSA1 = 2 × CSA2

The slant height of the later is twice that of the former.

⇒ 2 × l1 = l2

To find: the ratio of their radii

The curved surface area of cone = CSA = πrl

The ratio of their curved surface area

CSA1 : 2CSA2

= π × r1 × l1 : π × r2 × l2

= π × r1 × l1 : π × r2 × 2l1

= r1 : 2r2

⇒ CSA1 : 2CSA2 = r1 : 2r2

⇒ CSA1 / 2CSA2 = r1 / 2r2

∴ CSA1 / CSA2 = r1 / 4r2

∴ r1 / r2 = 1/4

Answer 2

Answer:

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