Question

The perimeter of sector OACB of the circle centred at O and of radius 24, is 73.12 cm. 

 (i) Find the central angle ∠AOB. 

(ii) Find the area of the minor segment ACB. (Use π = 3.14 and √3 = 1.73)

Answer 1

(i) Perimeter of sector = 2r + 2πrθ/360 = 73.12 

⇒ 2(24) + (2×3.14×24×θ)/360 = 73.12 

 ⇒ θ = 60° 

 (ii) Area of minor segment = [(3.14×24×24×60)/360 − 1.73/4 × 24 × 24)] cm² 

 = (301.44 − 249.12) cm² 

 = 52.32 cm²