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What is the ratio of the curved surface areas of two cones, if the diameters of their bases are equal and slant heights are in the ratio 3: 4?

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1 : 4

3 : 4

3 : 5

3 : 7

answer is B.

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Detailed Solution

Given- diameters of th bases are equal and slant heights are in the ratio 3: 4 of two cones.
Let

l 1

be the slant height of one cone.

l 2

be the slant height of other cone.
Then,

l 1 l 2 = 34 r 1 = r 2 = d 1 2 = d 2 2

Now,
Curved surface area

= π r l

C 1 C 2 = π r 1 l 1 π r 2 l 2 C 1 C 2 = 34

Thus, the ratio of the curved surface area is

3 : 4

.
Hence, option 2 is the correct option.

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