Question

In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° 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

It is given that the radius of circle, and angle at the centre of circle.

(i) We know that the Circumference C of circle of radius r is,

$\begin{array}{rcl}C& =& 2\mathrm{\pi r}\\ & =& 2\times \frac{22}{7}\times 6\\ & =& \frac{264}{7}\\ & =& 37.71\mathrm{cm}\end{array}$

(ii) We know that the Area A of circle of radius r is,

(iii) We know that the arc length l of a sector of an angle θ in a circle of radius r is

(iv) We know that the area A of a sector of an angle θ in the circle of radius r is given by