Question

Which of these is the area of a sector of a circle with r = 18”, given that its arc length is 6π?

Answer 1

22/7*18^2*6π/2π*18 = 169.65

Answer 2

`169.65\text{ inch}^2`

Explanation:

We have been given that the radius of our given circle is 18 inches and the arc length that corresponds to sector is 6 pi.

To find the area of our given sector we will use formula:

`\text{Area of sector}=\pi r^2*\frac{\text{Arc length}}{\text{Circumference of circle}}`

Upon substituting our given values in above formula we will get,

`\text{Area of sector}=\pi*18^2*(6\pi)/(2\pi*18)`

`\text{Area of sector}=\pi*324*(1)/(6)`

`\text{Area of sector}=\pi*54`

`\text{Area of sector}=169.64600329\approx 169.65`

Therefore, the area of our given sector is 169.65 square inches.