Diameter

Introduction to Circle

A circle is a two-dimensional plane figure. It is a collection of points in which all the points are equidistant from the center point  \( \text {O}\).

Learn more about the parts of a circle here.

 Circle is a collection of points equidistant from center

Here are some real-life examples of objects which are circular in shape.

  real life examples of circular objects


The Diameter of a Circle

The diameter of a circle is a straight line joining a point from one end of the circle to a point on the other end of the circle, passing through the center.

Look at this image.

a circle marked with diameter

Points A, B, M, N, P, Q, X, Y lie on the circle.

'AB' is the line segment which connects the point 'A'  and point 'B'  passing through the center 'O'.

This is the diameter.

Similarly, 'MN', 'PQ', 'XY' also pass through the center  'O'  joining the corresponding points on either side of the circle.

These line segments have the same length.

\(\text{AB = PQ = MN = XY}\)

Note that, 'OA', 'OB', 'OP', 'OQ', 'OM', 'ON', 'OX', 'OY' are half the length of the diameter.

This is called Radius (radii in plural). All radii of the same circle are equal in length.

Radius refers to the line drawn from the center of the circle to an endpoint on the circle.

We can derive the diameter formula from the circumference, the radius, and the area of the circle. Learn more about it here.


Diameter Symbols

Φ is the symbol for diameter.

The diameter of a circle is abbreviated as  'D', 'DIA', 'diam', 'dia',  'd'.

In lower case, diameter symbol is written as φ or ϕ.

 

symbol of diameter

The diameter symbol is commonly used in technical specifications and drawings.

A Φ\( 25\: \text {mm}\) means the diameter of the circle is \(25 \: \text {mm}\).


How do you find a Diameter?

Radius and diameter of the circle

Let us understand a few terms before we learn the diameter of a circle formula.

We just learnt that radius (\(\text{r}\)) is the length of the line segment from the center of the circle to an endpoint on the circle.

Circumference (\(\text{C}\)) refers to the enclosed boundary of the circle. We can say that it is the perimeter of the circle.

We can derive the diameter formula from circumference. Let us solve a few example sums here

A circle with radius, diameter and circumfrence

\(\text{C= \(\pi\)d}\)

where;

  • \(\text C\) is the circumference
  • \(\text d\) is the diameter
  • \(\pi\) is the constant \(3.14159...\)

The diameter formula when the radius is known is: 

  \( \text{Diameter} = 2 \times \text{radius}\)

\(\text {D = 2r}\)

The diameter formula using circumference is:

\( \text{Diameter} = \frac{\text{Circumference}}{\pi}\)

\[ \text{D}= \frac{\text{C}}{\pi}\]

The diameter formula when the area of the circle is known is :

\[\begin{align}
\text{Area of a circle (A)} &= \pi r^2 \\
\text {Diameter (D)} &= 2\text {r}
 \end{align}\]

Simplifying further, we get 

\(D  = 2 \sqrt{\frac{ \text {A}}{\pi}}\)

 
important notes to remember
Important Notes
  1. \(\ \pi\) is a mathematical constant which is the ratio of the circumference of a circle to its diameter. It is an irrational number often approximated to \( 3.14159\).
  2. Diameter divides the circle into two equal halves called semi-circles.
  3. Diameter of a circle formula with reference to Radius (r), Circumference(C) and Area (A) is 
        * \(\text {D = 2r}\)     
        * \(\text{D}= \frac{\text{C}}{\pi}\) 
        * \(D = 2 \sqrt{\frac{ \text {A}}{\pi}}\)    

Solved Examples

Example 1

   

 

The radius of a circle is \(5\: \text{cm} \). Calculate its diameter.

A circle of radius 5 centimeter

Solution:

We know that

\[\begin{align}
\text{Diameter} &= 2 \times \text{radius}\\
&= 2\times 5
 \end{align}\]

\[ \therefore  \text{Radius} = 3 \: \text {cm}\]
Example 2

 

 

The diameter of a circle is \(6\: cm \). What is the radius?

A circle of diamter 6 centimeter

Solution:

We know that

\[\begin{align}
 \text{Diameter} &= 2 \times \text{radius}\\
Radius &= \frac{D}{2}\\ &= \frac{6}{2} \\
&=3
 \end{align}\]

\[\therefore \text{Radius} = 3 \: \text {cm}\]
Example 3

 

 

The diameter of a circular swimming pool is \(7 \:\text {feet}\). What is the circumference of the swimming pool? Express your answer in terms of \(\ \pi\).

A circular pool of diameter 7 feet

Solution:

We know that circumference  a circle  

= \(\pi\ \times\text{d}\)

Therefore, Circumference of the swimming pool 

=\(\pi \times 7 \)

\[\therefore \text{Circumference} = 7 \pi\: \text {feet} \]
Example 4

 

 

John walks around a circular park of radius \(100\: \text{m} \). How many times should he walk around the park to cover at least \(3\: \text{km} \)? (use \(\ \pi\ = 3.14\))

 a circular park of radius 100 meter

Solution:

Radius of the park

\( =100\: \text{m}\) 

Diameter of the park

\[\begin{align}
   &= 2\times \text{r}\\
 &= 2 \times 100 \\
&=200 \: \text{m} 
 \end{align}\]

Circumference of the park 

\[\begin{align}
&=\pi\ \times \text{diameter}\\
&= \pi \times  200 \\
&= 3.14 \times 200 \\
&= 628 \:\text{m}
 \end{align}\]

John covers a distance of \(628 \: \text{m} \) by going around the park once.

By walking \(4\) rounds, he covers a distance of \( 628\times 4 = 2512 \: \text{m}\) only.

Instead, he has to go around the park \(5\) times to cover at least \(3 \:\text{km}\).

\[\therefore \text{John walks around the park}\: 5 \:\text{times.}\]
Example 5

 

 

Jack drew a circle of radius \(3\: cm \). Tim drew a circle whose radius is \(3\) times that of Jack's circle. What is the diameter of the circle drawn by Tim?

Jack and Tim's circle

Solution:

Radius of Tim's circle 

\[\begin{align}
&= 3\times 3 \\
&= 9 \: \text{cm}
\end{align}\]

Diameter  of Tim's circle 

\[\begin{align}
&=2 \times radius\\
  &= 2\times 9 \\
&= 18\: \text{cm}
 \end{align}\]

\[ \therefore \text{Diameter of Tim's circle} = 18 \:\text{cm}\]  

 
Challenge your math skills
Challenging Questions
  1. What is the perimeter of a semi-circle whose radius is \(7\: \text cm\)?
  2. A circular wheel has a diameter of \( 16 \:\text{cm}\). How far will it roll if it makes \(10\) revolutions? (Use \( \pi\ = 3.14\))
  3. If the diameter of a circle is doubled, how does this affect its area? 
  4. Find the ratio of the circumference of a circle to its area when the radius is \(1\: \text cm\). 

Practice Questions

Here are a few problems related to diameter.

Select/Type your answer and click the "Check Answer" button to see the result. 

 
 
 
 
 
 

Maths Olympiad Sample Papers

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

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Frequently Asked Questions (FAQs)

1. What is an example of a diameter?

If you observe the wheel of a cycle, the spikes run from one end to another end through the center.

We can relate this to the diameter of a circle, as the diameter is the line segment running from one end to the other end of the circle passing through the center.

2. What's the diameter of the circle?

The diameter of a circle is the longest chord of the circle. It is a line segment from one endpoint to another endpoint, passing through the center.

3. What is diameter and radius?

Radius refers to the line segment from the center of the circle to an endpoint on the circle. The diameter of a circle is twice the length of the radius, or it can be said that the radius is half the length of the diameter. 

\[ \text{Diameter} = 2 \:\times \: \text{radius}\]

  
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