SAT Math Problem (13)

Question

In the circle O which has a radius of 10, ∠AOB = ^2π/_5. What is the length of minor arc AB?

Answer 1

The angle AOB is one fifth of a full revolution; therefore its arc is one fifth of the circumference.

 

C = 2(pi)r = 20 pi; so the arc is 4pi in length.

Answer 2

The length of an arc of a circle, s, is given by:

 

s = rθ

 

where s = the arc length, r is the circle's radius, and θ is the central angle in radians that subtends the arc.  We know that r = 10 and θ = ∠AOB = 2π/5.  So:

 

s = rθ = 10*2π/5 = 4π ≅ 12.57