Question

A circular sector has an area of 50 in^2. The radius of the circle is 5 in.

What is the arc length of the sector?

Answer 1

Arc length = 10 unit

Explanation:

Given as,

The area of circular sector = 50 unit²

Radius of circle = 5 unit

∵ Area of circular sector =
`(\pi × r² × \Ф  )/(360)` ,Where Ф angle , r is radius of circular sector .

Length of sector =
`(\pi × r × \Ф  )/(180)`

So , Length of sector =
`(2 times Area of sector)/(radius)`

= [tex]\frac{2 times 50}{radius}[/5]

= 10 unit

Hence, arc length of sector = 10 unit Answer

Answer 2

Length of the arc = 1146.49 inches

Explanation:

Here, area of the sector = 50 sq inch

Radius = 5 in

Let the angle made by sector on the center = Ф

Now, area of the sector that makes an angle Ф :

Area =
`(\theta)/(360)  \pi  r^(2)`

or,
`50 = (\theta)/(360)  * 3.14 * 5^(2)`

⇒
`\theta = (50 * 360)/(3.14  * 5 * 5)  = 229.29`

hence, the angle subtended by the arc at the center is Ф = 229.29°

And the length of the arc = Фr

So, arc length = 229. 29 x 5 = 1146.49 inches