[Maths Class Notes] on Diameter Formula Pdf for Exam

Two times the length of a radius is equal to the diameter of a circle. The radius of a circle is measured from its centre to one of its endpoints, whereas the diameter is measured from one end of the circle to another end of the circle, passing through the centre.

The letter D represents the diameter. The circumference of a circle has an unlimited number of points, implying that the circle has an infinite number of diameters, each of which is of equal length.

Φ is a sign for a diameter that is used in engineering. In technical standards and drawings, this sign is frequently used. A value of Φ25 mm denotes a circle with a diameter of 25 mm.

Complete Representation of a Circle

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Formula and Example

The formula to calculate the diameter of a circle or a perfectly round-shaped figure describes the relationship between its diameter and the radius. The diameter is essentially composed up of two segments that are each a radius. Thus, the diameter formula is Diameter = 2 × the measurement of the radius. You can write this formula in shorthand as d = 2r.

That said, calculating a circle’s diameter is easy if we are familiar with the other dimensions of the circle i.e.: the radius, the circumference, or the area. However, calculating the diameter is still possible if you don’t know any of the above dimensions but you do have a sketch of the circle. 

We all know that a circle’s circumference is one of its components. Before we learn the formula for the diameter of a circle, let’s define a few concepts.

• The radius (r) is the length of a line segment connecting the circle’s centre and an endpoint.

• The enclosing boundary of the circle is referred to as the circumference (C). It’s also known as the circle’s perimeter. From the circumference and radius of the circle, we may calculate the diameter formula.

1. Diameter – Using Circumference

From the circumference, we can easily get the diameter formula. The circumference of a circle is calculated using the formula C = πd, where C = Circumference, d = Circle Diameter, and π = Constant (3.141)

Diameter = Circumference ÷ π

2. Diameter – Using Radius

The radius of a circle is the length of a line segment from the centre to an endpoint on the circle, and the diameter is twice the radius of the circle.

Hence, D = Radius × 2.

3. Diameter – Using Area of Circle

Area = π(Radius)².

Hence, 

D = 2 [sqrt{frac{A}{pi }}] is the formula for the diameter of a circle.

Example: Jill drew a circle of radius 3 units. What is the diameter of the circle?

Given circle’s Radius = 3 units

So, the diameter of the circle would be = 2 × Radius

= 2 × 3 = 6 units.

Thus, the circle’s diameter is 6 units.

How to Calculate Diameter

We can find out the diameter of a circle in the following ways:-

A. Calculate the Diameter of a Circle Using the Radius

If you already know the measure of the radius of the circle, just double it to get the diameter. The radius is the distance from the center point of the circle to its perimeter. As an example, if the radius of the circle is 7 cm, then the diameter of the circle is 7 x 2, or 14 cm.

B. Calculate the Diameter of a Circle Using Circumference

If you have the measurement of the circumference of a circle, divide it by π and you will get the diameter. The value of π is approximately equal to 3.14 but you must use the calculator to obtain the most accurate results. As an example, if the circumference of the circle is 25 cm, then the diameter is 25 cm/π, or 7.96 cm.

C. Calculate the Diameter of a Circle Using Area of the Circle

If you have the area of the circle, divide the outcome by π and find its square root in order to get the radius; then multiply by 2 to obtain the diameter. This slides back to maneuvering the formula to find the area of a circle i.e.: A = πr² to get the diameter. You can modify this into an area of a circle diameter formula as below:-

r = [sqrt{frac{A}{pi }}] cm.

As an example, if the area of the circle is 12cm², divide it by π and find the square root.

Using the diameter to area formula, we have [frac{12}{3.14}] = [sqrt{3.82}]

So the diameter of the circle is 1.95 x 2 = 3.90 cm.

Solved Examples

Example 1:

Find the diameter of a circle with a circumference of 32 cm

Solution 1:

To solve this problem, you will require the formula to find the circumference of a circle using the diameter i.e.

C = πd

Now, fill in the given details

32 = (3.14)d

Next, divide both sides by 3.14. Thus, 3.14 will neutralize on the right side of the equation, leaving d. Then divide 32 by 3.14 = 10.19

The answer is, the diameter is 10.19cm.

This also means that the radius is 5.09 cm [left ( frac{10.19}{2} right )]

Example 2:

The circumference of Susanne’s car tire is given 24 inches. Find out the diameter, closest distance traveled, in feet, after 3 full rotations of the tire?

Solution 2:

Given that the circumference = 24

Use the formula: C = πd

24 = πd

D= [frac{24}{3.14}] = 7.64 inches

The diameter is 7.64 inches

And the closest distance traveled after 3 full rotations = 24 x 3= 72inches

Since, we need to provide the answer in feet, convert the value to feet

12 inches = 1ft

Thus,

[frac{72}{12}] = 6feet

Conclusion

These are the different ways we can calculate the diameter of a circle and its mathematical representation. Learn how the terms are used to determine the formulas to calculate the diameter from the solved examples.