Question

In a circle of radius 6 cm, a chord of length 10 cm makes an angle of ${110}^{\circ }$ at the centre of the circle. Find

(i) The circumference of the circle.

(ii) The area of the circle

(iii) The length of the arc AB

(iv) The area of the sector OAB.

Answer 1

(i) Circumference $=2\pi r=2\times \frac{22}{7}\times 6=37.71cm$

(ii) Area of the circle $=\pi r^2=\frac{22}{7}\times 6\times 6=113.14c{m}^2$

(iii) Arc length $=2\pi r\times \frac{\theta }{{360}^o}$

$=37.71\times \frac{110}{360}=11.52cm$

(iv) Area of the sector $=\pi r^2\times \frac{\theta }{{360}^o}$

$=113.14\times \frac{110}{360}=34.57c{m}^2$