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Question

If the area of the sector of a circle with angle 45 is 11 cm2 , then the area of corresponding major sector is equal to.

A
88 cm2
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B
66 cm2
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C
77 cm2
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Solution

The correct option is C 77 cm2

Given, area of the sector of a circle with angle 45 is 11 cm2
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=88 cm2

Area of circle = Area of major sector + Area of minor sector
88 = Area of major sector + 11
Area of major sector = 88 - 11 =77 cm2

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