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The circle has center O. Its radius is 3 m, and the central angle a measures 60°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer

The Circle Has Center O Its Radius Is 3 M And The Central Angle A Measures 60 What Is The Area Of The Shaded RegionGive The Exact Answer In Terms Of Pi And Be S class=

Sagot :

Explanation

The area of a portion of a circle with radius 'r' and angle 'a' (in radians) is:

[tex]A_{\text{portion}}=\frac{1}{2}\cdot r^2\cdot a[/tex]

In this problem r = 3m, a = 60º.

First we have to express the angle in radians:

[tex]a=60º\cdot\frac{\pi}{180º}=\frac{1}{3}\pi[/tex]

The area of the shaded region is:

[tex]\begin{gathered} A=\frac{1}{2}\cdot(3m)^2\cdot\frac{1}{3}\pi \\ A=\frac{1}{2}\cdot9m^2\cdot\frac{1}{3}\pi=\frac{3}{2}\pi \end{gathered}[/tex]

Answer

The area is:

[tex]A=\frac{3}{2}\pi[/tex]

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