Question

A piece of wire 11 cm long is bent into the form of an arc of a circle subtending an angle of 45° at its centre. Find the radius of the circle.

Answer 1

ARC:

Arc is continuous piece of a Circle.

An angle subtended by an Arc at the centre of a circle is called its Central angle. In the circle smaller arc is called the minor arc and the larger arc is called the major Arc.

For minor arc the central angle is less than 180° while for major arc the central angle is  greater than 180°.

SOLUTION:

GIVEN :
Sector angle (θ) = 45°
Length of an Arc (l)= 11 cm

If the radius of a circle is r and length of the arc is l, then
Length of the arc (l) = (θ /180) × πr

11 =( 45/180) × (22/7) × r
11 = ¼ × 22r /7
11× 4 × 7 = 22r
r = (11 × 4 × 7)/22 = 2 ×7 = 14

r = 14

Hence, the Radius of the circle is 14 cm.

HOPE THIS WILL HELP YOU...

Answer 2

(thete/360) × 2 × pi × r = 11

r = 11×7×360/2×45×22

r = 14cm