Solved Examples on Arc of a circle
Example 1: Using 48 cm, determine the length of an arc of a circle that forms a 160° angle with the circle’s center.
Solution:
Given:
The value of π = 3.14
The value of θ = 160
The value of r = 48
The length of an arc = 2πr(θ/360)
= 2×3.14×48×160/360
= 133.97 cm.
Example 2: The radius of the circle is 18 units and the arc subtends 85° at the center. How long is the arc, measured in terms of circumference?
Solution:
We know that,
Circle Circumference = 2πr
C = 2π × 18
= 36π
Arc length = (θ/360) × C
= (85°/360°)36π
= (85°/360°)36×3.14
= 26.69 units
Arc length = 26.69 units
Example 3: In an arc with a radius of 20 cm and an angle subtended of 0.456 radians, determine its length.
Solution:
Given:
Radius (r) = 20
Radians (θ) = 0.456
Arc length = r θ
= 0.456×20
= 9.12 cm.
Example 4: A circle having a radius of 6 mm and a length of 15.06 mm should have an angle subtended by it.
Solution:
Given:
Arc length = 15.06 mm
Radius(r) = 6 mm
Arc length = r θ
15.06 = 6 θ
Divide both sides by 6.
2.51 = θ
Thus, the arc there subtends an angle of 2.51 radians.
Arc of a Circle
Arc of a Circle is a part of the circumference of a circle or we can also say the Arc of a Circle is some percentage of the circle’s circumference. As we know, a circle is defined as a two-dimensional geometrical object where all the points are equidistant from the center and the distance measured around the circle is known as a circumference and some portion of the circumference taken at a time is known as the Arc of a Circle.
In this article, we will learn the Arc of a Circle in detail, including its definition, types, and arc length formula. Other than that we will also discuss the angle subtended by an arc and the theorem related to this angle as well.
Table of Content
- What is the Arc of a Circle?
- Types of Arcs
- Arc of the Circle Formula
- How to Find Length of Arc of a Circle?
- Angle Subtended by Arc at Center