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

Given, 

Radius of circle = 6 cm 

Length of chord = 10 cm 

Angle subtend by chord = 110° 

(I). Circumference of circle = 2πr 

= 2 × 3.14 × 6 = 37.68 cm 

(II). Are of circle = πr² 

= 3.14 × 6× = 113.1 cm² 

(III). Length of arc = radius × angle subtend 

= 6 x \(\frac{120π}{180}\)

= 6 x \(\frac{2}3\times\frac{22}7\) = 11.51 cm

(IV). Area of sector = \(\frac{θ}{360}\timesπr^2\)

= \(\frac{110}{360}\times\frac{22}7\times6\times6\) = \(\frac{274}7\)

= 34.5 cm²