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

`12.6\pi\:\mathrm{km^2}\:\text{or }(63)/(5)\pi\:\mathrm{km^2}`

Explanation:

The area of a sector with measure
`\theta` in degrees is given by
`r^2\pi\cdot(\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(126)/(360)=\boxed{12.6\pi\:\mathrm{km^2}}`