(i) Radius of the circle r = 32 cm.
∴ Area of the circle = πr2
= \(\frac{22}{7}\) x (32)2
= \(\frac{22}{7}\) x 1024
= 32118.28 sq.cm.
(ii) ∠BAC = 60°
∴ ∠BOC = 120° (∵ Angle at the centre is double than the angle in the circumference).
Now, in ∆OBC, BC ⊥ OD,
∠BOD = ∠COD = 60°
∴ ∆ABC is an equilateral triangle.
Each side of this triangle,
a= 2 × 16√3 = 32√3cm
Area of equilateral triangle, ∆ABC :
(iii) Area of shaded region :
= Area of circle – Area of an equilateral ∆le
= 3218.28 – 1328.64
= 1889.6 sq.cm.