High School Math : How to find the area of a sector

Study concepts, example questions & explanations for High School Math

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Example Question #1 : How To Find The Area Of A Sector

In the figure, PQ is the arc of a circle with center O. If the area of the sector is 3\piwhat is the perimeter of sector?


Possible Answers:

3 + 2\pi

12 + \pi

6 + \pi

1 + \pi

12 + 2\pi

Correct answer:

12 + \pi


First, we figure out what fraction of the circle is contained in sector OPQ: \frac{30^{\circ}}{360^{\circ}}= \frac{1}{12}, so the total area of the circle is \dpi{100} \small 12\times 3\pi=36 .

Using the formula for the area of a circle, {\pi}r^{2}, we can see that \dpi{100} \small r=6.

We can use this to solve for the circumference of the circle, 2{\pi}r, or 12{\pi}.

Now, OP and OQ are both equal to r, and PQ is equal to \dpi{100} \small \frac{1}{12} of the circumference of the circle, or {\pi}.

To get the perimeter, we add OP + OQ + PQ, which give us 12+{\pi}.

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