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
