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Chapter 8: Q. 39 (page 541)

Consult the figure, which shows a circle of

radius r with center at O. Find the area K of the shaded region as a function of the central angleθ

Short Answer

Expert verified

The area isr22(sinθ+θ)

Step by step solution

01

Given information

We are given a figure

02

Find the area of sector And area of triangle

Area of sector can be given as

Ks=r2θ2

Area of triangle can be given as

Kt=12r×r×sin(π-θ)Kt=12×r2sinθ

03

Find the total area

TO find the total area add the area of sector or area of triangle

We get,

K=Ks+KtK=r22sinθ+r22θK=r22(sinθ+θ)

04

Conclusion

The area of shaded region isK=r22(sinθ+θ)

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