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The circle has center O. Its radius is 4 cm, and the central angle a measures 30°. 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 4 cm, and the central angle a measures 30°. What-example-1
User S G
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1 Answer

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Step-by-step explanation

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


A_{\text{portion}}=(1)/(2)\cdot r^2\cdot a

In this problem, the radius is r = 4cm, and the angle a = 30º.

First we have to express the angle in radians:


a=30º\cdot(\pi)/(180º)=(1)/(6)\pi

And now we can find the area of the shaded region:


\begin{gathered} A=(1)/(2)\cdot(4\operatorname{cm})^2\cdot(1)/(6)\pi \\ A=(1)/(2)\cdot16\operatorname{cm}^(2)\cdot(1)/(6)\pi=(4)/(3)\pi \end{gathered}

Answer

The area of the shaded region is:


A=(4)/(3)\pi cm^(2)

The circle has center O. Its radius is 4 cm, and the central angle a measures 30°. What-example-1
User TheJacobTaylor
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