Diameter of a Circle Definition, Formulas, and Steps
Diameter of a circle is the longest straight line passing through the center, touching two points on the circumference. Learn how to calculate it with formulas.
Shruti Dutta16 Dec, 2024
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The diameter of a circle is one of its most fundamental measurements. It is defined as the longest straight line that passes through the center of the circle, touching two points on its circumference.
Essentially, the diameter divides the circle into two equal halves. It is always twice the length of the radius, which is the distance from the center to any point on the circumference. The diameter of a circle plays a crucial role in various calculations involving circles, such as determining the circumference and area. Understanding the diameter is key to working with and solving problems related to circles in geometry and real-world applications.Also Check: Pie Chart
What is Diameter of a Circle?
The diameter of a circle is a line segment that passes through the center, with its endpoints lying on the circumference. In simpler terms, the diameter is the longest chord of the circle. The radius is the distance from the center to any point on the circle, and since the diameter is formed by two radii, it is twice the length of the radius. [video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Copy-of-Corurious-Jr-Reel-2-Landscape-1-2-1.mp4"][/video]Diameter Symbol
The symbol for diameter is typically represented by the letter
"d"
. It is often used in mathematical equations and geometric descriptions involving circles. For example, the formula for the diameter of a circle using the radius is:
d=2rd = 2rd=2r
Where:- d is the diameter
- r is the radius of the circle
Also Check: Ordinal Numbers
Diameter of Circle Formula
- The radius (r) is the distance from the center of the circle to any point on its boundary.
- The circumference (C) represents the perimeter or the boundary line of the circle.
- The area of a circle is the total space enclosed within its boundary. It is calculated using the formula ΟrΒ², where 'r' stands for the radius.
Steps for the Diameter of a Circle
Step 1 : Identify the radius (r) of the circle. Step 2 : Multiply the radius by 2. Formula : Diameter=2ΓRadius Example : If the radius is 5 cm, then: Diameter = 2Γ5 = 10 cmSteps to Find the Diameter Using the Circumference
Step 1 : Identify the circumference (C) of the circle. Step 2: Divide the circumference by Ο (approximately 3.14159). Formula : Diameter=Circumference π Example : If the circumference is 31.4 cm, then: Diameter=31.4π=31.43.14159β10cmFinding the Diameter Using the Area
Step 1 : Identify the area (A) of the circle. Step 2 : Use the area formula Area=ππ2, to find the radius first. Rearrange the formula to solve for radius (r): π=π΄π βStep 3 : Once you have the radius, multiply it by 2 to find the diameter. Formula : Diameter=2Γπ΄πβ β Example : If the area is 78.5 cmΒ², then: π=78.5πβ5cm βDiameter=2Γ5=10Also Check: Trapezium
Diameter of a Circle Using Radius
The diameter of a circle is simply twice the length of the radius. This is because the radius is the distance from the center of the circle to any point on its boundary, and the diameter is the distance across the circle, passing through the center. The formula to find the diameter (d) when the radius (r) is known is: Diameter=2ΓRadius Example : If the radius of a circle is 5 cm, then the diameter will be: π=2Γ5=10cmDiameter of a Circle Using Circumference
The circumference of a circle is the distance around the circle, or the perimeter. If you know the circumference (C) of the circle, you can calculate the diameter using the relationship between the two. The formula to find the diameter when the circumference is given is: Diameter=Circumferenceπ βWhere Ο (pi) is approximately 3.14159. Example : If the circumference of a circle is 31.4 cm, you can find the diameter by dividing the circumference by Ο: π=31.4πβ31.4/3.14159β10cm This tells you that the diameter is 10 cm.Diameter Formula Using Area of a Circle:
If you are given the area (A) of a circle, you can calculate the radius first and then find the diameter. The formula for the area of a circle is:Area=ππ2
Where r is the radius. To find the radius from the area, rearrange the formula to solve for r: π=Areaπ β Once you have the radius, the diameter is simply twice the radius: Diameter=2Γπ Example : If the area of the circle is 78.5 cmΒ², you can first find the radius by using the formula:π=78.5 π=78.5/3.14159β5cm Now, using the radius, calculate the diameter: π=2Γ5=10 cm So, the diameter of the circle is 10 cm.Also Check: Perimeter of a Triangle
[video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad.mp4"][/video]The Relationship Between Radius and Diameter
The radius and diameter are two fundamental measurements that define the size of a circle. They are directly related to each other, and understanding their relationship is crucial when working with various circle-related calculations. The diameter is always twice the length of the radius, while the radius is half of the diameter. Below is a table that highlights the key differences and relationships between the radius and diameter to help you better understand these concepts.| Aspect | Diameter | Radius |
| Definition | The diameter is a straight line that passes through the center of the circle and touches two points on the circumference. | The radius is the distance from the center of the circle to any point on its circumference. |
| Relationship | The diameter is twice the length of the radius. | The radius is half the length of the diameter. |
| Formula | d=2rd = 2rd=2r (Diameter = 2 Γ Radius) | r=d2r ={d}{2}r=2dβ (Radius = Diameter Γ· 2) |
| Length Comparison | The diameter is always greater than the radius. | The radius is always smaller than the diameter. |
| Position | The diameter extends from one side of the circle to the other, passing through the center. | The radius extends from the center of the circle to any point on the edge (circumference). |
| Size | The diameter is the longest chord of the circle, and it cuts the circle into two equal halves. | The radius is the shorter line compared to the diameter. |
| Relation to Circumference | The diameter is directly used in the formula for calculating the circumference: C=ΟdC = \pi dC=Οd. | The radius is used in the circumference formula as well: C=2ΟrC = 2\pi rC=2Οr. |
| Relation to Area | The diameter is not directly used in the area formula, but it is related because r=d2r = \frac{d}{2}r=2dβ. | The radius is used in the area formula: A=Οr2A = \pi r^2A=Οr2. |
| Measurement Example | If the diameter of a circle is 10 cm, then the radius is 102=5βcm\frac{10}{2} = 5 \, \{cm}210β=5cm. | If the radius of a circle is 5 cm, then the diameter is 2Γ5=10βcm2 \times 5 = 10\,{cm}2Γ5=10cm. |
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| What is an Abacus? | Math Puzzles |
| Multiplication Worksheets : | Multiplication Sums |
Diameter of a circle FAQs
What is the diameter of a circle?
The diameter of a circle is the longest straight line that passes through the center of the circle and touches two points on its circumference. It is twice the length of the radius.
How is the diameter related to the radius? The diameter is always twice the length of the radius. In other words, if you know the radius, you can find the diameter by multiplying it by 2. The formula is: π=2π Can the diameter be smaller than the radius?
No, the diameter is always larger than the radius. The diameter is exactly twice the length of the radius, so it is always longer.
Why is the diameter important in circle-related calculations?
The diameter plays a crucial role in calculating other important circle measurements, such as the circumference and area. Knowing the diameter allows you to quickly find these measurements using well-established formulas.
Can the diameter be smaller than the radius?
No, the diameter is always larger than the radius. The diameter is exactly twice the length of the radius, so it is always longer.
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