Diameter of a Circle is a line that travels through the centre and intersects the circumference at opposing ends. In other terms, the diameter of a circle is the line that goes through its centre and splits it into two equal sections. A circle's diameter is any straight line segment that travels through the centre of the circle and has endpoints on the circle's perimeter. The circle's diameter is referred to as its longest chord.
In this article, we will learn more about the diameter definition, the diameter formula, and how to calculate the diameter of a circle.
What is Diameter of a Circle?
The diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circumference of the circle. The diameter is also known as the longest chord of the circle.
The diameter is defined as twice the length of theradius of a circle. The radius is measured from the centre of a circle to one endpoint on the boundary of the circle, whereas, the distance of diameter is measured from one end of the circle to a point on the other end of the circle, passing through the centre.
Diameter of a circle is denoted by the letter D. There are infinite points on the circumference of a circle, this means that a circle has an infinite number of diameters, and each diameter of the circle is of equal length.
Read more about Circles.
Diameter of a Circle Definition
A circle's diameter is any straight line segment that travels through the centre of the circle and has endpoints on the circle's circumference. The circle's diameter is referred to as its longest chord.
Diameter Symbol
The diameter is defined by the letter D, but sometimes we also use the symbol Ø, to define the diameter of the circle, this symbol is mostly used in engineering and experimental purposes. We represent the diameter using this symbol i.e., Ø is 32 mm, which means the diameter of a circle is 32 mm.
The diameter formula may be derived from the circle's circumference, area, and radius.
Diameter of a Circle Using Circumference
The diameter of the circle using the circumference of the circle is calculated by the formula discussed below,
d = C ÷ π [As C = πd]
Where,
- C is the Circumference of the Circle,
- d is the Diameter of a Circle, and
- π is constant and its value is 22/7 or 3.142.
Check: Perimeter of the circle
Diameter of a Circle Using Radius
The radius of a circle is the distance between the circle's middle point and its circumference. The radius is symbolized by the lowercase letter r. The radius of the circle is twice the radius of the circle. Using this concept, the diameter formula is
d = 2r
Where,
- r is radius of the circle, and
- d is Diameter of the circle.
We may calculate the diameter of a circle using the area of a circle formula. The Area of a circle is symbolized by the uppercase letter A. The following is the equation to determine a circle's area:
A = πr2
⇒ A = π(d ÷ 2)2
⇒ A = (π x d2) ÷ 4
⇒ d2 = 4A÷ π
d = 2√A÷ π
Where,
- A is the Area of a circle,
- d is the Diameter of a circle, and
- π is the constant and its value is 22/7 or 3.142.
As a result, there exist three formulas for calculating the diameter of a circle:
- d = 2r
- d = C ÷ π
- d = 2√(A)÷ π
How to Find Diameter of a Circle?
If the radius, circumference, or area of a circle are specified, the diameter could be computed. To determine the diameter of a circle, follow the steps below:
Step 1: Determine the parameters given in the question i.e. radius, area, or circumference.
Step 2: Choose the proper formula from the three mentioned in the previous section.
Step 3: Put the value of the given parameter in the suitable formula and simplify the same to get the required answer.
As an example, let us use the above-mentioned formula to calculate the diameter. Consider the following example.
Example: Find the diameter of a circle with a radius of 10 units.
Solution:
Given: Radius of Circle = 10 units
Diameter of Circle = 2 × Radius
D = 2 × 10 = 20 units
Thus, the diameter of the circle is 20 units.
Relationship between Radius and Diameter of Circle
As previously stated, the length of the diameter is twice the radius. Diameter and radius have some similarities and variances. Before delving into the differences between diameter and radius, consider the similarities between them. Both diameter and radius are circle components that define features such as circle size, circumference, and area. Diameter = 2 x Radius is the equation that describes their connection.
Learn more about Radius of Circle.
To understand the differences between diameter and radius, look at the table added below.
Diameter vs Radius |
|---|
Radius | Diameter |
|---|
| Half of the diameter's length makes up the radius. | A circle's diameter is equal to twice its radius. |
| It begins in the center and ends at a point on the circumference of the circle. | It begins at the circle's boundary and finishes at the circle's boundary. |
| The radius has a shorter length than the diameter. | For each circle, the diameter is greater than the radius. |
Read More,
Solved Examples on Diameter of a Circle
Example 1:Determine the diameter of a circle with a radius of 8 units.
Solution:
Given,
Radius of the circle = 8 units
Diameter of the Circle = 2 × Radius
⇒ D = 2 × 8 = 16 units
Thus, the diameter of the circle is 16 units.
Example 2: Sham used a rope to form a circle. The circle's circumference is 628 cm. Assist him in determining the diameter of the circle.
Solution:
Given, Circumference = 628 cm
d = C ÷ π
⇒ d = 628 ÷ 3.14
⇒ d = 20
Thus, the diameter of Sham's rope circle is 20 cm.
Example 3: A circle has a surface area of 22.54 square cm. Determine the circumference of the circle.
Solution:
Given,
Area = 22.54 cm2
A = (π × d2) ÷ 4
⇒ 22.54 = (3.14 × d2 ) ÷ 4
⇒ 90.16 = 3.14 × d2
⇒ 28.71 = d2
⇒ √(28.71 )= d
⇒ 5.36 = d
Thus, the circle's diameter is 5.36 cm.
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