Diameter of a Circle

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Table of contents
  1. Introduction to the Diameter of Circle
  2. Definition of Diameter
  3. How to calculate diameter?
    1. Calculating Diameter Using Radius
    2. Calculating Diameter Using Circumference
    3. Calculating Diameter Using Area of a Circle
  4. Conclusion
  5. FAQs on Diameter of Circle

Introduction to the Diameter of Circle

The diameter of a circle is a term that often takes center stage in geometry. It is the longest straight-line distance across the circle, passing through its center and connecting two points on the circumference. This simple yet crucial concept serves as the foundation for understanding more complex mathematical relationships involving circles.

Definition of Diameter

A line segment whose endpoints lie on the circumference of the circle and passes through the centre of the circle is called the diameter of the circle.

The diameter is a crucial measurement for determining the size and scale of a circle. It provides information about the extent of the circle and helps establish its dimensions. By knowing the diameter, you can compare the size of a circle to other objects or circles.

In construction and engineering fields, the diameter is crucial for precise measurements and accurate placement of circular objects. It helps in designing and constructing structures involving circles, such as wheels, gears, pipelines, and circular foundations.

The diameter of a circle is a fundamental property that plays a vital role in various mathematical calculations, construction projects, and geometric concepts. It helps determine the size, scale, radius, circumference, and area of a circle, making it an essential element in numerous practical applications.

  • Diameter is denoted by "d".
  • It is twice the length of the radius of the circle.
  • It is the longest chord of the circle.
  • All the diameters of the circle have the equal length.
  • Diameter divides the circle into two equal parts called semicircles.
OABXYSTPQ

In the figure above, points A, B, X, Y, P, Q, S and T lie on the circumference of the circle with centre O. Hence, the line segments AB, XY, PQ and ST are diameters of the circle as these line segments are passing through the centre O, and all these diameters are equal.

AB=XY=PQ=ST

How to calculate diameter?

In this section, we will learn to find the length of the diameter of a circle. The diameter of a circle can be calculated using certain formulas based on what details are given.

Calculating Diameter Using Radius

Length of the diameter is twice the length of the radius. Hence if the radius of a circle is given, the diameter formula is expressed as

d=2r
where r is the length of the radius of the circle.

Example: If the radius of a circle is 7cm, calculate its diameter.
Given:r=7cm

To find: diameter of the circle

Solution:∵d=2r∴d=2×7∴d=14cmTherefore, the diameter of the given circle is 14cm.
Exercise:
  • Find the diameter of a circle if its radius is 8.5 cm.
  • Find the diameter of a car wheel whose radius is 12.5 inches.

Calculating Diameter Using Circumference

Circumference is the total length of the boundary of the circle and its formula is expressed as:
C=πd
where d is the diameter of the circle and π≈3.14.
If circumference is given, above formula can be used to calculate the diameter of the circle.
Example: Find the diameter of a circle if its circumference is 22cm.
Given:C=22cm

To find: diameter of the circle

Solution:∵C=πd∴Cπ=d∴d=Cπ∴d=223.14∴d=7.0063cm≈7.01cmTherefore, the diameter of the given circle is 7.01cm.
Exercise:
  • Find the diameter of a circle if its circumference is 33 km.
  • Find the diameter of a circular cake whose circumference is 188.4 cm.

Calculating Diameter Using Area of a Circle

Area of a circle is defined as the region occupied by the circle in a two-dimensional plane. It is determined by the formula below.
A=πr2
where r is the radius of the circle and π≈3.14.
If area of a circle is given, first we can calculate the radius of the circle using above formula, and then double the radius to get the diameter of the circle.
Example: If the area of the circle is 314cm2, find its diameter.
Given:A=314cm2

To find: diameter of the circle

Solution:First, lets calculate the radius of the circle using it's area.∵A=πr2∴Aπ=r2∴r2=Aπ∴r=Aπ∴r=3143.14∴r=100∴r=10cmTherefore, the radius of the given circle is 10cm.

Now, we know that diameter is twice the radius.

∵d=2r∴d=2×10∴d=20cmTherefore, the diameter of the given circle is 20cm.
Exercise:
  • If the area of the circle is 113.04mm2, find its diameter.
  • Area of the surface of the circular table is 25434cm2, find its diameter.
Conclusion Understanding the diameter is crucial in various mathematical and scientific applications, including geometry, physics, engineering, and more. It provides a fundamental measure of the size of the circle and serves as a basis for many circle-related calculations and analysis.

FAQs on Diameter of Circle

  • What is the diameter of a circle?

    The diameter is the straight-line distance across a circle, passing through its center and connecting two points on the circumference.

  • How is the radius related to the diameter?

    Radius is half of the length of the diameter.

    Radius=Diameter2

  • Can the diameter be shorter than the radius?

    No, the diameter is always twice the length of the radius, making it the longest straight-line distance in the circle.

  • Is the diameter always a straight line?

    Yes, the diameter is always a straight line that passes through the center of the circle.

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Radius of a Circle

Explore Radius of a Circle, its definition, learn how to calculate radius using various formulas along with solved examples.

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Circumference of a Circle

Explore diameter of a circle, learn how to find it using radius, circumference, and area.

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