Dhristi JEE 2022-24

Diameter – an Important Facet in Geometry

Geometry is a subject that is aligned with mathematics. Through this subject, we have learnt various shapes and figures, studied various of them. How does Geometry help us? Well, if you aspire to be an engineer then this is the first and basic step towards your aspiration. 

Diameter – is a topic picked up by us, as the importance of diameter in geometry cannot be overlooked or underestimated.  In this section we are going to learn about – Diameter, diameter definition, property, and formula of the same. We will also present solved examples in this content so that the students are benefitted. 


Diameter Meaning

The diameter is defined as twice the length of the radius of the circle. The radius is being measured from the centre of the circle to an endpoint of the circle, whereas, the distance of diameter is being measured from one end of the circle to another point on the other end of the circle, this will be done by passing it through the centre. The diameter here is denoted by the letter ‘D’. There are other infinite points on the circumference of a circle, which means that a circle has an infinite number of diameters, and each of these diameters of the circle is of an equal length.

Here we have learnt the diameter definition now we will learn the definition of diameter in other aspects as follows. 


Diameter Circle Definition

After learning the diameter meaning we need to observe and study the same in other aspects.

In Geometry, the circle is a 2D shape, where the collection of points which are on the surface of the circle are at an equidistant from the central point. The distance measured from the centre to any point on the surface is termed as radius. Similarly, the distance measured from one point on the surface of a circle to the other point on the surface of the circle passing through the centre is termed the diameter. While, in other words, the diameter is double the measure of the radius. Therefore, we can say that the diameter is the longest chord of the circle. The notations which are used to represent the diameter are ‘d’, ‘φ’, ‘D’, ‘Dia’.

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Diameter in a circle is the diameter which is a line that passes through the central point and meets the circumference which is located at both the ends. This is twice as long as the radius of the circle.


Diameter Definition Math 

In the simplest way defined – The diameter is the distance from one point of the circle through the centre of the circle to another point on the circle.
This is also the longest distance measured across the circle. Also, it is twice the radius.


Diameter Properties

The properties of the diameter of a circle are chalked down as follows:

  • The diameter is the longest chord of any circle.

  • The diameter chord divides the circle into two equal halves and thus it produces two equal semicircles.

  • The midpoint of the diameter is accurately the centre of the circle.

  • The radius is equal to half of the diameter.

Diameter Symbol

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Φ is the symbol that is used in the subject of engineering to represent the diameter. This symbol is being commonly used in technical specifications and drawings. A Φ25 mm means that the diameter of the circle is equal to 25 mm.


Diameter of a Circle Using Circumference

Here we can easily derive the diameter formula via the circumference of the circle. The formula for the circumference of a circle is C = πd; here, C denotes the Circumference, d is the Diameter of a circle, π denotes Constant (which is 3.141)

The diameter formula which is done using the circumference is: Diameter = Circumference ÷ π


Diameter of a Circle Using Radius

Radius is the length of the line segment which is from the centre of the circle to another endpoint on the circle and the diameter is twice is a measurement of the length of the radius of the circle. Here following the definition, the formula for the diameter is D = Radius × 2. We will discuss the formula of the diameter in the next section vividly. 

 

Diameter Formula

We all know that the diameter is a part of the circle. Now, let us understand a few related terms before we learn the formula for the diameter of the circle.

The radius (denoted as r) is the length of the line segment from the centre of the circle to an end-point on the same circle.

Circumference (denoted by C) refers to the enclosed boundary of the circle. This is called the perimeter of the circle. We are able to derive the diameter formula from the circumference and from the radius of the circle.

The different ways in order to calculate the diameter of a circle are given as below:

If the radius of a circle is known to us, then the diameter is calculated as follows:

D= 2R

Where “R” denotes the radius of the circle

Suppose the circumference of a circle is known, then the formula for calculating the diameter of the circle is

D = C/π

Where,

C is called the circumference of a circle

π is the constant value, which is approximately 3.14.

If we know the area of the circle, then the formula to compute the diameter of a circle is

D=4Aπ−−−√

(or)

D=2Aπ−−√

Where,

A is represented as the area of a circle

 

Solved Examples

Following are the problems to find the diameter of a circle.

Example 1:

If the diameter is 4 cm.

Solution:

Given:

Radius, R= 4 cm

We know that, if the radius is given, the formula to calculate the diameter is:

D = 2R.

Substitute R = 4 cm in the formula, we get

D = 2(4)

D = 8 cm.


Example 2:

The circumference of a circle is 30 cm. Calculate the diameter of a circle.

Solution:

Given:

Circumference, C = 30 cm.

We know that,

D = C/π

Now, substitute C = 30 cm and π= 3.14 in the formula,

D = 30/3.14

D = 9.55 (approximately)

Hence, the diameter of a circle is 9.55 cm (approximately).

FAQs on Diameter

Question 1. What is the 2D Shape?

Ans. A 2D which means the two-dimensional shape is a flat shape that has only two dimensions – that is length and width, there is no thickness or any depth in the figure. For example, on a sheet of paper, there are two dimensional shapes. This consists of a length and a width that does not have any depth or any specific or determined height.

Question 2. What is Geometry?

Ans. Geometry is a specific part or branch of mathematics which deals with the measurement, properties, and relationships of the points, lines, angles, solids and surfaces broadly. Geometry is classified as the study of properties of the specified elements which will remain invariant under the same specified transformations.

Question 3. What is Radius?

Ans. Radius is the line segment that extends from the centre of the circle or from the sphere to the circumference or to its bounding surface. 

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