Geometry homework

Question

Find the arc length of a swing set swing, if the chain is 8 feet long and the maximum angle you can swing is 90 degrees.

A. 2π ft

B. 3π ft

C. π Ft

D. 2 π ft

Answer 1

Because it can swing 90° and this is 1/4 of a circle of 360°, the circumference of the circle is 2πr = 2π8 = 16π and 1/4 of that is 4π feet.

This is none of the answers listed.

Answer 2

The length of the chain is the radius of the circle the swing set swing oscillates. Hence,

r = 8 ft

The maximum angle it can subtend is

θ_max = 90° = π/2 radians

The maximum arc length is,

s_max = rθ_max = (8 ft)(π/2 radians) = 4π ft