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(\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(126)/(360)=\pi\cdot(36mi^2\cdot126)/(360)=(63)/(5)\pi`

Thus the correct option is the 4th one:

`(63)/(5)\pi\text{ }mi^2`