Before we begin with the diameter formula, let us recall what is a diameter. Diameter is one of the important parts of a circle. The straight line connecting a point from one end of the circle to a point on the other end of the circle and passing through the center is called a diameter. Since there are infinite points on its circumference, this means that a circle has an infinite number of diameters and each diameter of the circle has an equal length..
What Is the Diameter Formula?
To understand the diameter formula. Let us consider the different cases of the Diameter Formula. We can find the diameter of a circle when the radius, area, or circumference is known.
Diameter Formula Using Radius of a Circle
Formula 1: The diameter is twice the length of the radius.
Diameter Formula = 2 × Radius
Diameter Formula Using Circumference of a Circle
Formula 2: The diameter is the ratio of circumference to π.
Diameter Formula = Circumference ÷ π
Diameter Formula Using Area of Circle
Formula 3: We can derive the diameter formula using the area formula which is
Area = π(Radius)2
Diameter Formula = 2√Area/π.
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Let us solve some interesting problems using the diameter formula.
Example1: Using the diameter formula find the diameter of a circle whose radius is 24 inches long.
We will use the first formula to find the diameter of the circle.
Diameter Formula =2×Radius
D=2×24 inches=48 inches
Answer: Diameter of the given circle = 48 inches.
Example 2: Find the diameter of a circle whose circumference is 8π units. Use diameter formula.
We will use the diameter formula of the circle when the circumference is given.
Diameter formula = Circumference/π = 8 units
Answer: The diameter of the given circle is 8 units.
Example 3: Using the diameter formula, can you determine the value of the radius if the diameter of a circle is 12 units?
Given : Diameter = 12 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 = 12 ÷ 2 = 6 units
Therefore, radius of circle is 6 units.
FAQs on Diameter Formula
What Is the Diameter Formula When Area of a Circle Is Known?
If the area of a circle is given in square units then it is easy to derive the diameter formula as given below:
Area = π(Radius)2
The formula for diameter = 2√Area/π.
What Is the Diameter 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 formula as given below:
Diameter formula = 2r.
The radius of the circle is half the diameter of the circle.
What Is the Diameter Formula When Circumference of a Circle Is Known?
If the circumference of a circle is given in 'C' units then it is easy to derive the diameter formula as given below:
Circumference, C = 2πr.
Diameter = 2r.
The formula for diameter = C/π units
How To Find Circumference With Diameter Formula?
If a diameter of a circle is given then by substituting the given values in the following diameter formula we can easily find the circumference of a circle.
The formula for diameter = Circumference/π.
C = πd units.