Question

What is the length of an arc if we know the radius of curvature is 12 in. and the area of the sector created is 252 in2?

Answer 1

The arc length is 42 in.

Explanation:

Hint-

`\text{Arc length}=r\theta\\\\\text{Sector area}=(1)/(2)\theta r^2`

when θ is radians.

Given here,

Sector area = 252 in²

Radius = 12 in

Putting the values,

`\Rightarrow \text{Sector area}=(1)/(2)\theta r^2`

`\Rightarrow 252=(1)/(2)\theta (12)^2`

`\Rightarrow 252=(1)/(2)\theta (144)`

`\Rightarrow \theta=(252*2)/(144)`

`\Rightarrow \theta=3.5\ rad`

Then the arc length will be,

`\text{Arc length}=12* 3.5=42\ in`

Answer 2

The equation to be used is

Area of sector = 0.5 x Radius of Circle * Length of Arc

Thus,

252 in2 = 0.5 x 12 in * Length of Arc

Length of Arc = 42 inches

I hope I was able to answer question. Have a good day.