Question

the radius of a circle in 6 miles. what is the area of a sector bounded by a 126° arc?

Answer 1

The area of a sector of a circle is:

$A=\pi r^2\cdot\frac{\theta}{360}$

Where θ is the angle of the arc and r is the radius.

In this case,

• r = 6mi

,

• θ = 126º

Then:

$A=\pi(6mi)^2\cdot\frac{126}{360}=\pi\cdot\frac{36mi^2\cdot126}{360}=\frac{63}{5}\pi$

Thus the correct option is the 4th one:

$\frac{63}{5}\pi\text{ }mi^2$