Question

The area of a circle is 18 pi square inches. If the area of a sector of this circle is 6 pi square inches, then

which of the following must be the sector's central angle?

Answer 1

120°

Explanation:

Area of a sector =
`(\theta)/(360) * \pi r^(2)\ where\ \pi r^(2) \ is\ the\ area\ of\ the\ circle`

theta is the sector's central angle

Area of the sector =
`(\theta)/(360) * \ area\ of\ a\ circle`

Given area of a circle = 18πin² and area of a sector = 6πin²

On substituting;

6π =
`\theta/360 * 18 \pi`

Dividing both sides by 18π we have;

1/3 =
`\theta/360`

`3 \theta = 360\\\theta = 360/3\\\theta = 120^(0)`

The sector's central angle is 120°