A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle
Solution:
Given, a piece of wire 20 cm long is bent into the form of an arc of a circle.
The arc of the circle subtends an angle of 60° at its centre.
We have to find the radius of the circle.
Length of the arc = θ/360°(2πr)
Given, length of the arc = 20 cm
20 = (60°/360°)(2)(22/7)r
20 = (1/6)(44/7)r
Solving for r,
20 = (22/21)r
r = 20(21)/22
r = 10(21)/11
r = 210/11
r = 19.09 cm
Therefore, the radius of the circle is 19.09 cm
✦ Try This: A piece of wire 40 cm long is bent into the form of an arc of a circle subtending an angle of 30° at its centre. Find the radius of the circle.
Given, a piece of wire 40 cm long is bent into the form of an arc of a circle.
The arc of the circle subtends an angle of 30° at its centre.
We have to find the radius of the circle.
Length of the arc = θ/360°(2πr)
Given, length of the arc = 40 cm
40 = (30°/360°)(2)(22/7)r
40 = (1/12)(44/7)r
Solving for r,
40 = (22/42)r
r = 40(42)/22
r = 76.36 cm
Therefore, the radius of the circle is 76.36 cm
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.3 Problem 16
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle
Summary:
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. The radius of the circle is 19.09 cm
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