Question

A neighborhood park is circular in shape. One sector of the park needs repairing, so officials would like to block off that portion with barricades. The area of the sector is 45 yd2, and . Find the length of one side of the barricades (i.e., the radius of the circle).

A.r = 6.71 yd
B.r = 15 yd
C.r = 30 yd
D.r = 45 yd

Answer 1

Area of the sector is: 45 π yd² and the central angle is 72° ( or 360° : 5 ). Therefore area of the circle is 5 times greater than the sector:
A = 5 · 45 π = 225 π yd²
A = r² π = 225 π
r = √225 = 15
Answer: B ) r = 15 yd.