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Question
If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm2, find its radius.
Solution
It is given that the curved surface area (C.S.A) of the cone is 286 cm2 and that the ratio between the base radius and the slant height is 7: 13. The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as
Curved Surface Area = πrl
Since only the ratio between the base radius and the slant height is given, we shall use them by introducing a constant ‘k’
So, r = 7k
l = 13k
Substituting the values of C.S.A, base radius, slant height and using `pi 22/7` in the above equation,
Curved Surface Area, 286 = `((22).(7k).(13k))/7`
286 = 286 k2
1 = k2
Hence the value of k = 1
From this we can find the value of base radius,
r = 7k
r = 7
Therefore the base radius of the cone is 7 cm .
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