A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of `240^@` .
This is an application of the arc length formula. It needs the angle in units of radians. So first convert the angle from degrees to radians. Then apply the arc length formula.
You can solve these types of problems by setting up a proportion:
`"arc length" / "circumference" = "central angle" / 360`
Since we're looking for the arc length, then we should have been given enough information to find the circumference and the central angle. We're told that the central angle = 240 but we need to find the circumference, `C=2pir` . Since the radius, r, is 4 inches, the circumference is `2pi(4)=8pi` .
We can now fill in some parts of our proportion:
`("arc length")/(8pi) = (240)/(360)`
Cross-multiply and simplify to get:
`"arc length" = (16pi)/3` or 16.755 inches
Finding the area of a sector has a similar setup as well. Hope this helped and good luck.