how to find the diameter
Diameter of a Circle
In a circle, diameter is a line that passes through the center and meets the circumference at each end. It is twice as long as that of the radius of the circle.
| 1. | What Is the Diameter of a Circle? |
| 2. | Diameter of Circle Formula |
| 3. | How to Calculate the Diameter of a Circle? |
| 4. | FAQs on Diameter |
What Is the Diameter of a Circle?
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circumference of a circle. The diameter is also known as the longest chord of the circle.
Diameter Definition
The diameter is defined as twice the length of the radius of a circle. The radius is measured from the center of a circle to one endpoint of the circle, whereas, the distance of diameter is measured from one end of the circle to a point on the other end of the circle, passing through the center. The diameter is denoted by the letter D. There are infinite points on the circumference of a circle, this means that a circle has an infinite number of diameters, and each diameter of the circle is of equal length.
Observe the following figure which shows the diameter of a circle by a blue line. The yellow line from the center to one endpoint of the circle is the radius and the outer boundary which is marked by a black dotted curve is the circumference of the circle.
Diameter Symbol
Φ is the symbol that is used in engineering to represent diameter. This symbol is commonly used in technical specifications and drawings. A Φ25 mm means the diameter of the circle is 25 mm.
Diameter of Circle Formula
We all know that diameter is a part of a circle. Let us understand a few terms before we learn the formula for the diameter of a circle.
- The radius (r) is the length of the line segment from the center of the circle to an endpoint on the circle.
- Circumference (C) refers to the enclosed boundary of the circle. It is also known as the perimeter of the circle. We can derive the diameter formula from the circumference and the radius of the circle.
Diameter of a Circle Using Circumference
We can easily derive the diameter formula from the circumference. The formula for the circumference of a circle is: C = πd; here, C = Circumference, d = Diameter of a circle, π = Constant (3.141)
The diameter formula using circumference is: Diameter = Circumference ÷ π
Diameter of a Circle Using Radius
Radius is the length of the line segment from the center of the circle to an endpoint on the circle and diameter is twice the length of the radius of the circle. Using this definition, the formula for the diameter is: D = Radius × 2.
Diameter Formula Using Area of Circle
We can derive the diameter of a circle formula using the area of the circle formula that is area = π(Radius)2. Hence, the diameter of the circle formula using area, D = 2√Area/π.
How to Calculate the Diameter of a Circle?
The diameter of a circle can be calculated if the radius or the circumference is given.
Let us try using the formulas mentioned above in a practical illustration to find the diameter. Observe the example given below.
Example: Jack drew a circle of radius 3 units. What is the diameter of the circle?
Solution:
Given: Radius of the circle = 3 units
The diameter of the circle is = 2 × Radius
= 2 × 3 = 6 units.
Therefore, the diameter of the circle is 6 units.
☛Articles Related to Diameter of a Circle
Check out these interesting articles to know more about the diameter of a circle and its related topics.
- Chords and Diameters
- How to find the radius and diameter of a circle
- Ratio of Circumference of a Circle to its Diameter
- Circumference to Diameter
Diameter Examples
-
Example 1: The radius of a circle is 15 units. Calculate its diameter.
Solution:
Given, radius = 15 units
We know that,
Diameter = 2 × radius
= 2 × 15
Therefore, diameter = 30 units. -
Example 2: Can you determine the value of the radius if the diameter of a circle is 36 units?
Solution:
Given : Diameter = 36 Units
We know that diameter is twice the value of the radius. This means the radius is half of the value of the diameter.
Diameter = 2 × Radius
R = D ÷ 2
Radius = 36 ÷ 2 = 18 units
Therefore, radius = 18 units -
Example 3: The diameter of a circular swimming pool is 7 feet. What is the circumference of the swimming pool? Express your answer in terms of π.
Solution:
Given : Diameter = 7 feet
We know that circumference of a circle = π × d
Thus, Circumference of the swimming pool = π × 7
Therefore, circumference = 7π feet.
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FAQs on Diameter
What Is the Diameter?
A diameter is a straight line that passes through the center of a circle and divides the circle into two sections. It is the longest chord of the circle that meets the circumference at each end.
Which Symbol is Used to Represent Diameter?
The symbol used to represent the diameter in engineering is ⌀. It is often referred to as "phi". This phi symbol is used to describe the diameter of a circular section. For example, "⌀20" means the diameter of a circle is 20 units in dimensions.
What Are Radius and Diameter?
The radius and diameter of a circle are two important parts of a circle that are interdependent on each other. The radius of a circle is a line segment that starts from the center of a circle and ends at the circumference of the circle. It is half the length of the diameter of a circle, i.e., Radius = Diameter/2. The diameter of a circle is a line segment that passes through the center of a circle and has two endpoints at the circumference. It is twice the length of the radius of a circle, i.e., Diameter = 2 × Radius.
How To Calculate Diameter?
The diameter of a circle can be calculated according to the given parameters. If the parameters like radius, circumference, or area are given then we can directly use the following formulas.
- Diameter = Circumference ÷ π (when the circumference is given)
- Diameter = 2 × Radius (when the radius is given)
- Diameter = 2√[Area/π] (when the area is given)
What Is an Example of a Diameter?
If you observe the wheel of a cycle, the spikes run from one end to another end through the center. We can relate this to the diameter of a circle, as the diameter is the line segment that starts from one end of a circle and ends at the other end of the circle passing through the center.
How To Find the Diameter From Circumference?
If the circumference of a circle is known then we can easily find the value of the diameter by substituting the values in the formula: Diameter = C ÷ π; where 'C' is the circumference and π is a constant whose value is 3.14.
How To Find the Area of a Circle With the Diameter?
The area of a circle is calculated with the help of the formula: πr2. If the diameter is given we can find the radius by dividing the value of diameter by 2. After getting the radius, we can substitute its value in the formula: πr2 to get the area of the circle or directly apply the area formula with diameter, A = π(d/2)2 = πd2/4
What is the Use of Diameter to Circumference Calculator?
The diameter to circumference calculator is an online tool used to determine the value of the circumference of a circle. In the diameter to circumference calculator enter the dimension of the diameter and get the value of circumference within a few seconds. You can also try the diameter calculator for direct calculations.
What Is the Diameter of a Circle Formula When Radius of a Circle Is Known?
If the radius of a circle is given in 'r' units then it is easy to determine the diameter of the circle formula. With the definition of radius, we know that it is half of the diameter hence, the diameter formula = 2r.
What Is Half of a Diameter of a Circle Called?
The diameter of a circle is a line segment from one end of the circle to the other end of the circle passing through the center of the circle. Whereas, the radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle. Hence, the radius is half of the diameter of a circle.
How is Diameter Related to the Radius of the Circle?
The radius of a circle is half the diameter. The relation between radius and diameter can be mathematically expressed in the formula: Diameter = 2 × radius.
Is Diameter Half of Radius?
No, the diameter is not half of the radius; it is twice the radius of a circle. It is represented by the formula: Diameter = 2 × Radius.
how to find the diameter
Source: https://www.cuemath.com/geometry/diameter/
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