Diameter of a Circle

Last updated on 09 February 2025

Table of contents

Introduction to the Diameter of Circle
Definition of Diameter
How to calculate diameter?
Conclusion
FAQs on Diameter of Circle

Introduction to the Diameter of Circle

The diameter of a circle is a term that often takes center stage in geometry. It is the longest straight-line distance across the circle, passing through its center and connecting two points on the circumference. This simple yet crucial concept serves as the foundation for understanding more complex mathematical relationships involving circles.

Think of the diameter as the lifeline of a circle, it not only defines its size but also plays a pivotal role in calculations involving circumference, area, radius and more. The relationship between the diameter and the radius is straightforward yet profound, as the diameter is always twice the radius.

The diameter is a cornerstone for many real-world applications. Whether it’s measuring the size of a wheel, designing a circular table, or calculating the size of circular structures, the diameter simplifies these tasks. In technology, engineering, and even art, understanding the diameter is vital for precision and symmetry.

What makes the diameter fascinating is its ability to connect the theoretical and practical aspects of geometry. It helps bridge abstract mathematical formulas with tangible, everyday applications. Beyond its technical importance, the diameter also introduces us to beautiful relationships, such as its role in defining the constant π (pi), the ratio of a circle's circumference to its diameter.

Definition of Diameter

A line segment whose endpoints lie on the circumference of the circle and passes through the centre of the circle is called the diameter of the circle.

The diameter is a crucial measurement for determining the size and scale of a circle. It provides information about the extent of the circle and helps establish its dimensions. By knowing the diameter, you can compare the size of a circle to other objects or circles.

In construction and engineering fields, the diameter is crucial for precise measurements and accurate placement of circular objects. It helps in designing and constructing structures involving circles, such as wheels, gears, pipelines, and circular foundations.

The diameter of a circle is a fundamental property that plays a vital role in various mathematical calculations, construction projects, and geometric concepts. It helps determine the size, scale, radius, circumference, and area of a circle, making it an essential element in numerous practical applications.

Diameter is denoted by "d".
It is twice the length of the radius of the circle.
It is the longest chord of the circle.
All the diameters of the circle have the equal length.
Diameter divides the circle into two equal parts called semicircles.

In the figure above, points A, B, X, Y, P, Q, S and T lie on the circumference of the circle with centre O. Hence, the line segments AB, XY, PQ and ST are diameters of the circle as these line segments are passing through the centre O, and all these diameters are equal.

AB = XY = PQ = ST

How to calculate diameter?

In this section, we will learn to find the length of the diameter of a circle. The diameter of a circle can be calculated using certain formulas based on what details are given.

Calculating Diameter Using Radius

Length of the diameter is twice the length of the radius. Hence if the radius of a circle is given, the diameter formula is expressed as

d = 2 r

where

r

is the length of the radius of the circle.

Example: If the radius of a circle is

7 cm

, calculate its diameter.

Given:

r = 7 cm

To find: diameter of the circle

Solution:

\begin{array}{lrcl} ∵ & d & = & 2 r \\ ∴ & d & = & 2 \times 7 \\ ∴ & d & = & 14 cm \end{array}

Therefore, the diameter of the given circle is

14 cm

Exercise:

Find the diameter of a circle if its radius is 8.5 cm.
Find the diameter of a car wheel whose radius is 12.5 inches.

Calculating Diameter Using Circumference

Circumference is the total length of the boundary of the circle and its formula is expressed as:

C = π d

where

d

is the diameter of the circle and

π \approx 3.14

If circumference is given, above formula can be used to calculate the diameter of the circle.

Example: Find the diameter of a circle if its circumference is

22 cm

Given:

C = 22 cm

To find: diameter of the circle

Solution:

\begin{array}{lrcl} ∵ & C & = & π d \\ ∴ & \frac{C}{π} & = & d \\ ∴ & d & = & \frac{C}{π} \\ ∴ & d & = & \frac{22}{3.14} \\ ∴ & d & = & 7.0063 cm \approx 7.01 cm \end{array}

Therefore, the diameter of the given circle is

7.01 cm

Exercise:

Find the diameter of a circle if its circumference is 33 km.
Find the diameter of a circular cake whose circumference is 188.4 cm.

Calculating Diameter Using Area of a Circle

Area of a circle is defined as the region occupied by the circle in a two-dimensional plane. It is determined by the formula below.

A = π r^{2}

where

r

is the radius of the circle and

π \approx 3.14

If area of a circle is given, first we can calculate the radius of the circle using above formula, and then double the radius to get the diameter of the circle.

Example: If the area of the circle is

314 {cm}^{2}

, find its diameter.

Given:

A = 314 {cm}^{2}

To find: diameter of the circle

Solution:First, lets calculate the radius of the circle using it's area.

\begin{array}{lrcl} ∵ & A & = & π r^{2} \\ ∴ & \frac{A}{π} & = & r^{2} \\ ∴ & r^{2} & = & \frac{A}{π} \\ ∴ & r & = & \sqrt{\frac{A}{π}} \\ ∴ & r & = & \sqrt{\frac{314}{3.14}} \\ ∴ & r & = & \sqrt{100} \\ ∴ & r & = & 10 cm \end{array}

Therefore, the radius of the given circle is

10 cm

Now, we know that diameter is twice the radius.

\begin{array}{lrcl} ∵ & d & = & 2 r \\ ∴ & d & = & 2 \times 10 \\ ∴ & d & = & 20 cm \end{array}

Therefore, the diameter of the given circle is

20 cm

Exercise:

If the area of the circle is $113.04 {mm}^{2}$ , find its diameter.
Area of the surface of the circular table is $25434 {cm}^{2}$ , find its diameter.

Conclusion Understanding the diameter is crucial in various mathematical and scientific applications, including geometry, physics, engineering, and more. It provides a fundamental measure of the size of the circle and serves as a basis for many circle-related calculations and analysis.

FAQs on Diameter of Circle

What is the diameter of a circle?
The diameter is the straight-line distance across a circle, passing through its center and connecting two points on the circumference.
How is the radius related to the diameter?
Radius is half of the length of the diameter.
$Radius = \frac{Diameter}{2}$
Can the diameter be shorter than the radius?
No, the diameter is always twice the length of the radius, making it the longest straight-line distance in the circle.
Is the diameter always a straight line?
Yes, the diameter is always a straight line that passes through the center of the circle.
How many diameters can a circle have?
A circle has infinitely many diameters, as any line segment passing through the center of the circle and touching the circumference on both sides is a diameter.
How do you calculate the diameter if the radius is known?
Diameter can be calculated using below formula if radius is given.
$Diameter = 2 \times Radius$
How is the diameter used to calculate the circumference?
Circumference can be calculated using below formula if diameter is given.
$Circumference = π \times Diameter$
How do you find the diameter if the circumference is given?
Diameter can be calculated using below formula if circumference is given.
$Diameter = \frac{Circumference}{π}$
How is the diameter used in constructing circular objects?
The diameter helps determine the size, dimensions, and symmetry of the circular object, ensuring precision in construction.
Why is the diameter important in real-world measurements?
The diameter simplifies the measurement and design of circular objects, such as wheels, pipes, and round tables.
What role does the diameter play in the concept of π (pi)?
π (pi) is defined as the ratio of a circle's circumference to its diameter.
$π = \frac{Circumference}{Diameter}$
What are some interesting facts about the diameter?
- The diameter is the longest distance across the circle.
- Any chord that passes through the center is a diameter.
- Diameter is used to define the concept of π.

Diameter of a Circle

Introduction to the Diameter of Circle

Definition of Diameter

How to calculate diameter?

Calculating Diameter Using Radius

Calculating Diameter Using Circumference

Calculating Diameter Using Area of a Circle

FAQs on Diameter of Circle

What is the diameter of a circle?

How is the radius related to the diameter?

Can the diameter be shorter than the radius?

Is the diameter always a straight line?

How many diameters can a circle have?

How do you calculate the diameter if the radius is known?

How is the diameter used to calculate the circumference?

How do you find the diameter if the circumference is given?

How is the diameter used in constructing circular objects?

Why is the diameter important in real-world measurements?

What role does the diameter play in the concept of π (pi)?

What are some interesting facts about the diameter?

Radius of a Circle

Circumference of a Circle