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Question
In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.
Solution
Let the length of the major arc be x cm
Radius of the circle = 10.5 cm
∴ Length of the minor arc`=x/5 "cm"`
Circumference `= (x + x/5) = "6x"/5 "cm"`
Using the given data, we get :
`(6x)/5 = 2xx22/7xx21/2`
`=>(6x)/5 = 66`
Or.
x = 55
∴ Area of the sector corresponding to the major arc `= (1/2xx55xx21/2) = 288.75 "cm"^2`
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