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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 angle胃

Short Answer

Expert verified

The area isr22(sin胃+胃)

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=r2胃2

Area of triangle can be given as

Kt=12r脳r脳sin(蟺-胃)Kt=12脳r2sin胃

03

Find the total area

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

We get,

K=Ks+KtK=r22sin胃+r22胃K=r22(sin胃+胃)

04

Conclusion

The area of shaded region isK=r22(sin胃+胃)

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