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

1.	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» 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

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»

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