## What is the diameter of a circle & how to find one?

We have learned about two types of shapes in Geometry – two-dimensional shapes and three-dimensional shapes. Two-dimensional shapes only have two dimensions, such as length and width, whereas three-dimensional shapes have three dimensions. Shapes differ in terms of length, breadth, slant height, surface area, etc. 3D shapes also have height. They are described by length, height, surface area, etc. Circular shapes are defined by their parameters, including “Diameter”.

The radius of a circle is the distance from the center point to the points on the surface of the circle. A circle is a 2D shape, made up of points that are equidistant from the center. Similarly, the diameter is the distance from one point on a circle’s surface to the next point on the circle’s surface through the center. In other words, the diameter is twice the radius. In simple terms, the diameter of circle is its longest chord. Diameters are represented by letters d, φ, D, and Dia.

In a circle, the diameter can be defined as any segment of a straight line that passes through its center and ends on the circle itself. As a line segment, a chord of a circle can join any two points on its circumference. The diameter of a circle is the largest chord of the circle and one that passes through its center. The radius measures the distance from the center to the edge of the circle. If the radius is 4 cm, then the diameter will be 4 cm x 2, or 8 cm. If you know the circumference, divide it by the diameter.

## The formula for the diameter of a circle:

You can calculate a circle’s diameter in different ways based on its radius:

If the radius of a circle is known, the diameter is calculated as follows:

D= 2R, Where “R” is the radius of circle.

Circles have circumferences, so the diameter can be calculated based on the circumference.

D = C/π, where C is the circumference of a circle &π= 22/7 or 3.14

Using the area of a circle as input, the diameter of a circle can be calculated using the following formula:

D=√4A/ π or,

D=2√A/π, where A is the area of the circle.

## Properties of the diameter of a circle:

• Circles are measured by their diameter, which is the longest chord.
• Two equal semi-circular segments are produced by dividing the circle by the diameter.
• Circles should have a radius of half of their diameter
• The center is defined as the midpoint of the diameter.

### Examples:

1. Find the diameter of a circle if its radius is 6 cm.

Ans-Given:

We know that the radius is given. The formula to calculate the diameter is:

D = 2R.

Substitute R = 6 cm in the formula, we get

D = 2(6)

D = 12 cm.

1. The circumference of a circle is 36 cm. Calculate the diameter.

Given:

Circumference, C = 16cm.

We know that,

D = C/π

Now, substitute C = 16 cm and π= 3.14 in the formula,

D = 16/3.14

D = 5.09 (approximately)

Hence, the diameter of a circle is approximately equal to 5.09 cm.

1. Determine the diameter of a circle, given that the area is 120 cm2.

Given:

Area of a circle, A = 120 cm2.

If the circle’s area is given, then the formula to calculate the diameter of a circle is given by:

D=2√A/π

Now, substitute the value of A and π in the formula, we get

D=2√120/3.14

D= 2(6.19)

D = 12.38 (approximately)

Thus, the diameter of a circle is 12.38 cm.

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