# What is the area of a sector of a circle that has a diameter of 10 in. if the length of the arc is 10 in?

Jul 14, 2015

I found: Surface: $S = 25$ in^2

#### Explanation:

The area $S$ of your "slice" is:
$S = \frac{1}{2} {r}^{2} \theta$
where:
$r = \frac{10}{2} = 5$ in is the radius
$\theta$ is the angle in radians formed by your slice.

You can find the angle remembering that the arc length $l$ is:
$l = r \theta$
so that $\theta = \frac{10}{5} = 2 r a d$
finally:
Surface: $S = \frac{1}{2} \left({5}^{2}\right) \cdot 2 = 25$ in^2