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# Diameter Formula

Many objects in our daily life in round or circular shape. Some objects of this shape are a ball, wheel, bangle, clock etc. Geometrically such objects are called a circle or sphere in two dimensional and three dimensional respectively. These objects are having one fixed point around which the complete object will exist, known as the centre. Distance from one endpoint to another endpoint on the boundary through the centre is referred to as diameter. In this article, we will discuss diameter, some other related terms and Diameter formula with examples. Let’s start learning!

## Diameter Formula

### What is the Diameter?

A circle is a particular shape of the objects. A circle is a type of closed shape. It is the set of all points in a plane which are at a given distance from a given point. So, the distance between two points on the circumference through the centre will always be a constant, which is known as the diameter of the circle. Therefore, we may connect a point on the circumference on a circle to the given centre.

Diameter formula can be easily derived by doubling the radius of the circle. Diameter can also be computed if we know the length of the circumference of the circle or area of the circle. Thus a unique circle will have a unique value of diameter. Source: en.wikipedia.org

### Some Important Terms Related to a Circle

1. Centre: It is a point as a pivot in the circle. It is used to draw the circle.
2. Circumference: It is the set of points that are at an equal distance around the centre of the circle.
3. Radius: It is the distance from the centre to any point on the circumference.
4. Diameter: It is the distance between any two points on the circumference measured through the centre. It is double in the length that the length of the radius.
5. Area: Area of the circle describes the amount of space covered by the circle. So, it will give the coverage of circle as a two-dimensional plane.

### Formulas for Diameter:

Let us now discuss the different methods to compute the diameter of a circle. We need anyone value out of its diameter, circumference or area. The formula in terms of diameter, circumference, and the area is,

• If we know the diameter $$D = R \times 2$$
• When know the circumference $$D = \frac{C}{ \pi}$$
• If we know the area of a circle $$D =2 \times \sqrt(\frac{A}{\pi}$$
 R the radius of the circle D the diameter of the circle C the circumference of the circle A the area of the circle $$\pi$$ 3.14

## Solved Examples for Diameter Formula

Q.1: Find the value of the diameter of the circle whose radius is 15 cm?

Solution: As given in the problem,

The radius of the circle, R = 15 cm

Thus using the formula,

$$D = R \times 2$$

Substituting the value of the radius,

$$D = 15 \times 2$$

R = 30 cm

Q.2: Find the diameter of a circle whose area is 300 square cm?

Solution: As given in the problem,

Area of the circle, A = 300 square cm

Now applying the formula,

$$D =2 \times \sqrt(\frac{A}{\pi}$$

Substituting the value of are we will get,

$$D = 2 \times \sqrt(\frac{ 300 }{\pi}$$

$$= 2 \times \sqrt(\frac{ 300 }{ 3.14 }$$

= $$2 \times 9.77 cm$$

=  19.54 cm

Thus diameter value will be 19.54 cm.

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