Diameter

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 Definition

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 point of the circle, this will be done by passing it through the centre.

The diameter 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 of a Circle

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’.

Image View of Diameter 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

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 $C=\pi d$ here, C denotes the Circumference, d is the Diameter of a circle, $\pi$ denotes Constant (which is 3.141)

The diameter formula which is done using the circumference is: Diameter = Circumference$\div\pi$

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 $\mathtt{Diameter} = \mathtt{Radius}\times 2$. We will discuss the formula of the diameter in the next section vividly.

Diameter Formula Using Area of Circle

The diameter of a circle formula can be derived using the formula of area of the circle i.e, $\mathtt{Area} (A) = \pi \times \mathtt{Radius}^{2}. $Now by substituting the value of radius as $\dfrac{D}{2}$, we get, $\dfrac{A}{\pi}$, $\frac{A}{\pi} = (\frac{D}{2})^{2}$.

$\Rightarrow \frac{D}{2} = \sqrt{\frac{A}{\pi}} \\$

$\Rightarrow D = 2\times \sqrt{\frac{A}{\pi}}$

Hence, the diameter of the circle formula using area, $D = 2\times \sqrt{\frac{A}{\pi}}$, where A is an area.

Solved Examples

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

Example 1: Find the diameter of a circle if its radius is 6 cm.

Solution:

Given radius, R= 6 cm

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

D = 2R.

Substitute R = 6 cm in the formula, we get

D = 2(6)

D = 12 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,

$D =\dfrac{C}{\pi}$

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

$D =\dfrac{30}{3.14}$

D = 9.55 (approximately)

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

Example 3: The diameter of a circular swimming pool is 7 feet. What is the circumference of the swimming pool? Answer in terms of π.

Solution:

Given: Diameter = 7 feet

We know that circumference of a circle = $\pi\times d$

Thus, Circumference of the swimming pool = $\pi\times 7$

Therefore, the circumference of the pool = $7\pi $ feet.

Practise Problems

1. Find the radius and diameter of the following circle.

A) Radius 9 cm, Diameter 18 cm

B) Radius 18 cm, Diameter 9 cm

C) Radius 36 cm, Diameter 18 cm

D) Radius 16 cm, Diameter 38 cm

2. Find the radius and diameter of the following circle.

A) Radius 23 m, Diameter 98 m

B) Radius 12 m, Diameter 24 m

C) Radius 24 m, Diameter 24 m

D) Radius 22 m, Diameter 23 m

3. Identify the radius, diameter, and chord from a given circle.

A) Radius LK, Diameter MK

B) Radius LK, Diameter MN

C) Radius LK, Diameter KN

D) Radius MN, Diameter LK

Answers

1) A

2) B

3) B

Conclusion

In this article we have learnt that 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. Diameter is twice the radius of the circle. We also learnt about the diameter using circumference,radius and area of the circle. Hope you liked it!