Question

In the given figure, O is the centre of a circle of radius 7 cm. AB is a chord of the circle. Find the perimeter of the shaded region (with central angle $6 0^{\circ}$ ).

Approach

Triangle AOB is equilateral (since central angle $6 0^{\circ}$ and radii equal), so $A B = 7$ cm. Arc length = $\frac{60}{360} \times 2 π r = \frac{1}{6} \times 2 \times \frac{22}{7} \times 7 = \frac{22}{3}$ cm. Perimeter of shaded region = arc + chord = $\frac{22}{3} + 7 = \frac{43}{3}$ or $14.33$ cm.

Step-by-step working

1
Recognize equilateral triangle AOB, so $A B = 7$ cm
0.5 marks
2
Calculate arc length $= \frac{22}{3}$ cm
0.5 marks
3
Perimeter $= \frac{22}{3} + 7 = \frac{43}{3}$ cm
0.5 marks
4
Express as $14.33$ cm (if needed)
0.5 marks

Concepts used

arc lengthperimetersectorcircle geometry

Approach

Step-by-step working

Concepts used

Similar question types