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

Answer:

Length of the arc =  1146.49 inches

Step-by-step 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 = $\frac{\theta}{360}  \pi  r^{2}$

or,  $50 = \frac{\theta}{360}  \times 3.14 \times 5^{2}$

⇒ $\theta = \frac{50 \times 360}{3.14  \times 5 \times 5}  = 229.29$

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

Answer 2

Answer:

Arc length = 10 unit

Step-by-step explanation:

Given as,

The area of circular sector = 50 unit²

Radius of circle = 5 unit

∵ Area of circular sector = $\frac{\pi × r² × \Ф  }{360}$  ,Where Ф angle , r is radius of circular sector .

Length of sector = $\frac{\pi × r × \Ф  }{180}$

So , Length of sector = $\frac{2 times Area of sector}{radius}$

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

                                   = 10 unit

Hence, arc length of sector = 10 unit    Answer