Question

Find the arc length and area of a sector with radius r=13 inches and central angle theta =40 degrees

Answer 1

The arc length and the area of the circle sector are approximately 9.076 inches and 58.992 square inches.

Explanation:

Geometrically speaking, we determine the arc length (
`s`), in inches, and the area (
`A`), in square inches, of a circle sector by means of these formulas:

`s = 2\pi\cdot \left((\theta)/(360)\right)\cdot r` (1)

`A = \pi \cdot \left((\theta)/(360) \right)\cdot r^(2)` (2)

Where:

`r` - Radius, in inches.

`\theta` - Central angle, in sexagesimal degrees.

If we know that
`\theta = 40^(\circ)` and
`r = 13\,in`, then the arc length and the area of the circle sector are, respectively:

`s = 2\pi\cdot \left((40)/(360) \right)\cdot (13\,in)`

`s \approx 9.076\,in`

`A = \pi \cdot \left((40)/(360) \right)\cdot (13\,in)^(2)`

`A = 58.992\,in^(2)`

The arc length and the area of the circle sector are approximately 9.076 inches and 58.992 square inches.