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Question
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. Find the ratio of their radii.
Solution
Let slant height of the first cone = l
Then slant height of the second cone = 2l
Radius of the first cone = r1
Radius of the second cone = r2
Then, curved surface area of first cone = πr1l
Curved surface area of second cone = πr2(2l) = 2πr2l
According to given condition:
πr1l = 2(2πr2l)
π πr1l = 4πr2l
r1 = 4r2
`r_1/r_2 = 4/1`
∴ r1 : r2 = 4 : 1
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