If the area of the sector of a circle with angle 45∘ is 11cm2 , then the area of corresponding major sector is equal to.
A
88cm2
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B
66cm2
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C
77cm2
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Solution
The correct option is C77cm2
Given, area of the sector of a circle with angle 45∘ is 11cm2
In the above figure, green portion represents a minor sector and yellow portion represents a major sector.
So, angle of minor sector (θ)=45∘
Area of minor sector =θ360×πr2 ⇒11=45360×227×r2 ⇒11=18×227×r2 ⇒r2=11×8×722=28 ⇒r2=28
Now, area of circle =πr2=227×28 ⇒ Area of circle=88cm2
∵ Area of circle = Area of major sector + Area of minor sector ⇒ 88 = Area of major sector + 11 ⇒ Area of major sector = 88 - 11 =77cm2