Question

The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?

Give the exact answer in simplest form.

____ square kilometers. (pi, fraction,)​

Answer 1

Answer:

$12.6\pi\:\mathrm{km^2}\:\text{or }\frac{63}{5}\pi\:\mathrm{km^2}$

Step-by-step explanation:

The area of a sector with measure $\theta$ in degrees is given by $r^2\pi\cdot\frac{\theta}{360}$, where $r$ is the radius of the sector.

What we're given:

• $r$ of 6
• $\theta$ of $126^{\circ}$

Substituting given values, we get:

$A_{sec}=6^2\pi \cdot\frac{126}{360}=\boxed{12.6\pi\:\mathrm{km^2}}$