Solved Examples on Arc
Example 1: Find the length of the Arc if the radius of the circle is equal to 4cm and the angle formed by the Arc is equal to π/16 radians.
Solution:
Given:
- Radius of the circle = 4cm
- Arc Angle = π/16 radians
Since the Arc Angle is in radians, we can utilize the Arc Length formula, i.e.,
L = θ × r
⇒ L = (π/16) × 4
⇒ L = π/4 cm.
Example 2: Determine the length of the Arc if the Central Angle is equal to 65 degrees with a radius of 12 cm
Solution:
Given;
- Radius of the circle = 12 cm
- Arc Angle= 65 degrees
Using the Arc Length (L) formula for the measure of the angle given in degrees.
L = θ×(π/180°)×r
⇒ L = 65°×(π/180°)×12
⇒ L = 39π/9 cm.
Example 3: If the diameter of a circle is 10 cm and the measure of the angle is 105˚, find the length of the Arc?
Solution:
Given;
- Diameter of the circle = 10 cm
- Arc Angle=105 degrees.
Using the diameter formula for Arc Length calculation,
Arc Length(L) =(θ/360°)×π×d
⇒ L = (105°/360°)×π×10
⇒ L = 105π/36 cm.
Example 4: The door width is 1500mm, the side height is 1950mm and total height at center is 2200mm.Find the radius of Arc.
Solution:
The Arc width is 1500mm
The Arc height is 2200 − 1950 = 250mm
Radius of Arc can be calculated as:
Radius = {2502 + (1500/2)2 }/8 × 250
⇒ Radius = 312.5cm
What is Arc of a Circle?
Arc is a segment of the circumference of a circle or any curved shape. An Arc in geometry is any smooth curve connecting two specific points. Arc is a smooth curve linking these endpoints. The length of an Arc is known as its Arc length. In Mathematics, it commonly refers to a portion of a circle, but it can also be parts of other shapes such as spheres, ellipses, and cylinders.
In this article, we will discuss the introduction, definition, types, and application of an Arc and its meaning. We will also understand measures and formulae to calculate the Arc Length and Arc Angle in mathematics. We will also solve various examples and provide practice questions for a better understanding of the concept of this article.
Table of Content
- What is Arc in Math?
- Arc of a Circle
- Types of Arcs
- Angle of Arc
- Measures of an Arc
- Arc Formula