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Question
The diameter of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.
Solution 1
Let radius of each cone = r
Ratio between their slant heights = 5 : 4
Let slant height of the first cone = 5x
And slant height of second cone = 4x
Therefore, curved surface area of the first cone = πrl = πr × (5x) = 5πrx
Curved surface area of the second cone = πrl = πr × (4x) = 4πrx
Hence, ratio between them = 5πrx : 4πrx = 5 : 4
Solution 2
Let their slant height be 5x and 4x.
Given that diameter of two cones are equal
∴ R1 = R2 = R
S1 = πRl = πR(5x)
S2 = πRl = πR(4x)
`(S_1)/(S_2) = (πR (5x))/(πR (4x)) = 5/4`
`(S_1)/(S_2) = 5/4`
S1 : S2 = 5 : 4.
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