Two arcs have the same length. One arc is intercepted by an angle of 3pi/2 radians in a circle of radius 15 cm. If the radius of the other circle is 25 cm, what central angle intercepts the arc?

Question

Two arcs have the same length. One arc is intercepted by an angle of  radians in a circle of radius 15 cm. If the radius of the other circle is 25 cm, what central angle intercepts the arc?

a.  radians

b.  radians

c. radians

d.  radians

Answer 1

s=rθ is the relationship between arc length s, circle radius r, and subtended angle θ.

If the arc lengths of two arcs are the same:

r₁θ₁=r₂θ₂. If r₁=15cm, θ₁=3π/2, r₂=25cm, θ₂=r₁θ₁/r₂=(45π/2)/25=9π/10 (answer option b).