Diameter Formula
The line dividing a circle into two equal parts, each known as a semicircle, is known as the diameter. The circle’s centre serves as its diameter’s midpoint. This indicates that it splits the diameter in half, noting the radius of each half. The length of a diameter is equal to twice the length of the radius. To find the diameter of a circle, the Diameter Formula is used. The Diameter Formula is given by 2 × R, R being the radius. Learn more about diameter formula and how to calculate diameter in this article.
What is Diameter?
The diameter of a circle is a straight line segment that passes through its center and ends on the circle’s boundary. It is the circle’s longest chord, twice as long as the radius.
Characteristics of Diameter
- Straight Line: The diameter is a straight line segment.
- Center of Circle: It passes through the center of the circle.
- Endpoints on the Circle: The endpoints of the diameter lie on the circumference of the circle.
- Twice the Radius: The diameter is always twice as long as the radius of the circle.
Diameter Formula
The diameter of a circle is a fundamental geometric property that is directly related to the radius of the circle. The formula for the diameter (d) can be derived from the radius (r) and is given by:
D = 2r
Where, r is the radius
Diameter Formula Using Radius of a Circle
If the radius of a circle is known, the diameter can be found using the formula:
D = 2r
Diameter Formula using Circumference
The diameter of a circle can be derived from its circumference using the following formula:
d=C/π
Where, C is circumference
Diameter Formula with Area of Circle
The diameter of a circle can be derived from its area using the following formula:
\[ d = 2 \sqrt{\frac{A}{\pi}} \]
where:
- \( d \) is the diameter of the circle.
- \( A \) is the area of the circle.
- \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159.
Derivation
The area of a circle is given by the formula:
\[ A = \pi r^2 \]
To find the diameter from the area, we first need to express the radius (\(r\)) in terms of the area. Rearrange the area formula to solve for \(r\):
\[ r^2 = \frac{A}{\pi} \]
\[ r = \sqrt{\frac{A}{\pi}} \]
Since the diameter (\(d\)) is twice the radius:
\[ d = 2r = 2 \sqrt{\frac{A}{\pi}} \]
Example Using Diameter Formula
Example 1. If the area of a circle is 50 square centimeters, find the diameter
Solution:
Diameter can be calculated as follows:
\[ d = 2 \sqrt{\frac{50}{\pi}} \approx 2 \sqrt{\frac{50}{3.14159}} \approx 2 \sqrt{15.92} \approx 2 \times 3.99 \approx 7.98 \text{ cm} \]
Example 2: If the circumference of a circle is 31.4 cm, Find the diameter
Solution:
the diameter can be calculated as follows:
\[ d = \frac{31.4}{\pi} \approx \frac{31.4}{3.14159} \approx 10 \text{ cm} \]
Example 3: If the radius of a circle is 5 cm, Find the diameter is:
Solution:
The diameter is
\[ d = 2 \times 5 = 10 \text{ cm} \]