Question

For a circle of radius 8 feet, find the arc length s subtended by a central angle of 3π​ radians. Round to the nearest hundredth.

a) 4.19 feet
b) 12.57 feet
c) 16.38 feet
d) 25.13 feet

Answer 1

To find the arc length, use the formula s = rθ, where s is the arc length, r is the radius, and θ is the central angle in radians. Substituting the given values, we find that the arc length is approximately 75.36 feet.

Step-by-step explanation:

To find the arc length, we can use the formula:

s = rθ

where s is the arc length, r is the radius of the circle, and θ is the central angle in radians.

In this case, the radius is 8 feet and the central angle is 3π radians. Substituting these values into the formula, we get:

s = 8(3π)

To find the approximate value, we can use the approximation π ≈ 3.14. So:

s ≈ 8(3)(3.14)

s ≈ 75.36 feet

Rounding to the nearest hundredth, the arc length is approximately 75.36 feet.