Area of a Sector

**magentarita** · August 15th 2008, 02:48 AM

Find the area of a sector of a circle of radius 3cm formed by an angle of 60 degrees. Round answer to two decimal places.

**Tom1234** · August 15th 2008, 04:26 AM

the area of a sector is 1/2 *r^2* a in radians.
pi radians=180 deagrees -> pi/3 rad=60 degrees.
so S=(3^2*pi/3)/2=1.5pi

**Chop Suey** · August 15th 2008, 07:45 AM

To find the area of a sector of a circle:

$\frac{\theta_{\deg}}{360} \cdot A$

Area of a circle is:

$A = \pi r^2$

If you want to do it using radians like Tom1234 suggested:

Here's how you convert from radians to degrees and vice versa:

$\frac{\theta_{\deg}}{180} = \frac{\theta_{\text{rad}}}{\pi}$

Then:

$\frac{\theta_{\text{rad}}}{2\pi} \cdot \pi r^2 = \frac{\theta_{\text{rad}}}{2}\cdot r^2$

**magentarita** · August 15th 2008, 12:42 PM

Wonderful job!

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