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 inches squared?

Answer 1

42 inches

Explanation:

Area =`pixxr^2`
Area of sector=`(theta)/360xxpixxr^2`

`252=(theta)/360xxpixx12^2`

`[252xx360]/(144pi)=theta`

`theta=630/pi`

Circumference=`piD`

Arc length=`(theta)/360xxpixxD`

Arc length =`((630)/pi)/360xxpixx24`

Arc length=`630/360xx24`

Arc length=`7/4xx24`

Arc length=`7xx6`