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 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

 

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Answer 2

Answer:

The arc length is 42 in.

Step-by-step explanation:

Hint-

$\text{Arc length}=r\theta\\\\\text{Sector area}=\dfrac{1}{2}\theta r^2$

when θ is radians.

Given here,

Sector area = 252 in²

Radius = 12 in

Putting the values,

$\Rightarrow \text{Sector area}=\dfrac{1}{2}\theta r^2$

$\Rightarrow 252=\dfrac{1}{2}\theta (12)^2$

$\Rightarrow 252=\dfrac{1}{2}\theta (144)$

$\Rightarrow \theta=\dfrac{252\times2}{144}$

$\Rightarrow \theta=3.5\ rad$

Then the arc length will be,

$\text{Arc length}=12\times 3.5=42\ in$