Diameter - Explanation, Formula, and Examples
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
(ImagewillbeUploadedSoon)
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.
FAQs on Diameter Formula
1. What are a circle and its quick facts?
A circle is a round, two-dimensional form that looks like the letter 'O.'
A circle's circumference includes an arc.
The area between a chord and the arc it joins is known as a segment.
A tangent is a straight line that intersects one of the circle's points.
When two radii meet, they form a sector, which is the region between them.
A circle's complete arc measures 360 degrees.
A semicircle is a shape that forms half of a circle and has an arc of 180 degrees.
2. What is the Surface Area of Circle Formula?
A circle's surface area is the same as the circle's area. When we talk about a circle's area, we're referring to its overall surface area. The area occupied by the surface of a 3-D form is known as surface area. A sphere's surface is spherical, but a circle is a simple flat 2-dimensional shape.
If the radius, diameter, or even the circumference of the circle are known, the surface area can be calculated. Square units are used to represent it.
3. What is the Derivation of the Area of the circle?
Example:
Consider a circle that has been divided into 12 equal sectors.
Take one sector and divide it into two equal halves once more. There will be 13 sectors in the circle presently.
Let's rearrange the 13 sectors into a rectangular shape, adjusting each inverted form alternatively.
The height of the structure will be equal to the circle's radius as soon as it is completed.
The width will be equal to half of the circle's curved portions. In other terms, it is roughly half the circle's circumference.
Now, Since, Circumference = 2 × π × radius
And, width is = Half the Circumference = π × radius
So, to get the area of the rectangle, multiply the width by the height.
Area = (π × radius) × (radius)
= π × radius²
4. What is the real-life example of Perimeter?
Perimeter is derived from the Greek terms peri, which means "around," and metron, which means "measure." A two-dimensional shape's perimeter is the total length of its sides.
When hanging up Christmas lights around the home or fencing the backyard garden, we frequently come across the perimeter. Other instances are determining the overall length of a soccer field's boundary or the length of crochet or ribbon required to cover a table mat's border.
5. What are some daily life examples of sectors of a circle?
The origin of a sector is always the circle's centre. The region of a circle encompassed by its two radii and the arc adjoining them is known as the sector of a circle.
A slice of pizza is one of the most common real-life examples of a sector's area. The slices of a circular pizza are shaped like a sector. Examine the diagram below, which depicts a pizza divided into 6 equal slices, each of which represents a sector, and the pie's radius is 7 inches.