Question

What is the length of an arc cut off by an angle of 1.5 radians on a circle of radius 8 inches?

Answer 1

To solve this problem, we should first recall that the circumference is the measure of the total arc enclosing the circle. The formula for circumference is:

Circumference = 2 π r

where r is the radius of the circle

 

Now since we are only looking for a fraction of the arc, not the total arc, therefore this simply means we are finding for a portion of the circumference. Now we use the formula:

Arc length = (θ / 360) * 2 π r

Where θ/360 represents how much of the fraction is the arc

 

Convert angle to degrees: θ = 1.5 rad (180° / π rad) = (270/π)°

 

Therefore the arc length is:

Arc length = (270/π / 360) * 2 π (8 inches)

Arc length = 12 inches