Diameter of a Circle

The diameter of a circle is a line that travels through the centre and intersects the circumference at opposing ends.

• It splits the circle into two equal sections.
• It is also referred to as its longest chord.
• It is twice the radius.
• For example, if a circle has a radius of 5 cm, then its diameter is: d = 2 × 5 = 10 cm.

Diameter of Circle Formulas

The diameter formula may be derived from the circle's circumference, area, and radius.

Using Radius

The radius of a circle is the distance between the circle's center and its circumference. The radius is symbolized by the lowercase letter r. The radius of the circle is twice the radius of the circle. Using this concept, the diameter formula is

\large d = 2r

Where,

• r is radius of the circle, and
• d is Diameter of the circle.

Using Circumference

The diameter of the circle using the circumference of the circle is calculated by the formula discussed below,

{\large d = \dfrac{C}{\pi} }

Where,

• C is the Circumference of the Circle,
• d is the Diameter of a Circle, and
• π is constant and its value is 22/7 or 3.142.

Check: Perimeter of the circle

Using Area of a Circle

We may calculate the diameter of a circle using the area of a circle formula. The following is the equation to determine a circle's area:

{\LARGE d = 2 \sqrt{\frac{A}{\pi}} }

Where,

• A is the Area of a circle,
• d is the Diameter of a circle, and
• π is the constant and its value is 22/7 or 3.142.

The Area of a circle is symbolized by the uppercase letter A.

A = πr²

⇒ A = π(d ÷ 2)²

⇒ A = (π x d²) ÷ 4

⇒ d² = 4A÷ π

As a result, there exist three formulas for calculating the diameter of a circle:

• d = 2r
• d = C ÷ π
• d = 2√(A)÷ π

Steps to find Diameter of a Circle

If the radius, circumference, or area of a circle is specified, the diameter could be computed. To determine the diameter of a circle, follow the steps below:

Step 1: Determine the parameters given in the question i.e. radius, area, or circumference.

Step 2: Choose the proper formula from the three mentioned in the previous section.

Step 3: Put the value of the given parameter in the suitable formula and simplify the same to get the required answer.

As an example, let us use the above-mentioned formula to calculate the diameter. Consider the following example.

Example: Find the diameter of a circle with a radius of 10 units.

Solution:

Given: Radius of Circle = 10 units

Diameter of Circle = 2 × Radius

D = 2 × 10 = 20 units

Thus, the diameter of the circle is 20 units.

Radius vs Diameter

To understand the differences between diameter and radius, look at the table added below.

Read More,

• Equation of a Circle
• Chords of a Circle

Key Properties of Diameter

• The diameter is defined as twice the length of the radius of a circle (d = 2r).
• The radius is the distance from the centre to any point on the circle.
• The diameter spans across the circle through the centre.
• The diameter of a circle is denoted by the letter D, but sometimes we also use the symbol Ø.
• A circle has an infinite number of diameters because there are infinite points on the circumference.
• Each diameter is of equal length.

Solved Examples on Diameter of a Circle

Example 1: Determine the diameter of a circle with a radius of 8 units.

Solution:

Given,

Radius of the circle = 8 units

Diameter of the Circle = 2 × Radius

⇒ D = 2 × 8 = 16 units

Thus, the diameter of the circle is 16 units.

Example 2: Sham used a rope to form a circle. The circle's circumference is 628 cm. Assist him in determining the diameter of the circle.

Solution:

Given, Circumference = 628 cm

d = C ÷ π
⇒ d = 628 ÷ 3.14
⇒ d ≅ 200

Thus, the diameter of Sham's rope circle is 200 cm.

Example 3: A circle has an area of 22.54 square cm. Determine the circumference of the circle.

Solution:

Given,

Area = 22.54 cm²

A = (π × d²) ÷ 4

⇒ 22.54 = (3.14 × d² ) ÷ 4
⇒ 90.16 = 3.14 × d²
⇒ 90.16/ 3.14 = d²
⇒ 28.71 = d²
⇒ √(28.71 = d
⇒ 5.36 = d            

Thus, the circle's diameter is 5.36 cm.