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# Diameter Formula

The **diameter formula** is used to find the length of the diameter of a circle. Before we begin with the diameter formula, let us recall what is a diameter. Diameter is one of the important parts of a circle. The straight line connecting a point from one end of the circle to a point on the other end of the circle and passing through the center is called a diameter. Since there are infinite points on its circumference, this means that a circle has an infinite number of diameters and each diameter of the circle has an equal length.

## What is the Diameter Formula?

There are different ways in which the diameter formula of a circle can be expressed. Let us consider the different cases of the Diameter Formula. We can find the diameter of a circle if we know the radius, the area, or the circumference of the circle.

### Diameter Formula Using Radius of a Circle

The diameter is twice the length of the radius. Therefore, the diameter formula using the radius is expressed as:

Diameter = 2 × Radius

### Formula of Diameter from Circumference

The circumference of a circle is π times the diameter of the circle which means, Circumference = Diameter × π. Therefore, the diameter formula using the circumference is expressed as:

Diameter = Circumference ÷ π

### Diameter Formula with Area of Circle

We can derive the diameter formula using the formula for the area of a circle which is

Area = π(Radius)^{2}

Now, we can rewrite the above formula in terms of radius, that is, Area = π(Radius)^{2}, can also be written as, Radius = √(Area/π)

Now, once we know the radius, we can find the diameter because we know that Diameter = 2 × Radius

So, when Radius = √(Area/π), then the diameter will be, Diameter = 2 × √(Area/π). Therefore, the diameter formula using the area of a circle is expressed as, Diameter = 2√(Area/π)

## Examples on Diameter Formula

Let us solve some interesting problems using the diameter formula.

**Example 1:** Using the diameter formula find the diameter of a circle whose radius is 24 inches long.

**Solution:**

We will use the following diameter formula to find the diameter of the circle.

Diameter = 2 × Radius

D = 2 × 24 = 48 inches

**Answer: **The diameter of the given circle = 48 inches.

**Example 2:** Find the diameter of a circle whose circumference is 8π units. Use the diameter formula.

**Solution:**

When the circumference is given, we can use the following diameter formula. Diameter = Circumference/π. After substituting the value of the circumference as 8π, we get Diameter = 8π/π. This gives the value of diameter as 8 units.

**Answer:** The diameter of the given circle is 8 units.

**Example 3:** Using the diameter formula, can you determine the value of the radius if the diameter of a circle is 12 units?

**Solution:**

Given: Diameter = 12 Units

We know that the diameter is twice the value of the radius. This means the radius is half of the value of the diameter.

Diameter = 2 × Radius

Radius = Diameter ÷ 2

Radius = 12 ÷ 2 = 6 units

Therefore, the radius of the circle is 6 units.

## FAQs on Diameter Formula

### What is the Diameter Formula When the Area of a Circle Is Known?

If the area of a circle is given, then it is easy to derive the diameter formula, Area = π(Radius)^{2}. After substituting the value of the given area, the radius can be calculated. Once the radius is calculated, the diameter can be calculated using the formula, Diameter = 2 × Radius. Let us understand this using the following steps:

- Step 1: We know that the formula for the area of a circle is, Area = π(Radius)
^{2} - Step 2: Now, we can rewrite the above formula in terms of radius as Radius = √(Area/π)
- Step 3: Now, once we know the radius, we can find the diameter because we know that Diameter = 2 × Radius
- Step 4: So, when Radius = √(Area/π), then the diameter will be: Diameter = 2√(Area/π). Therefore, the diameter formula using the area of the circle will be, Diameter = 2√(Area/π)

### What is the Diameter Formula When the Radius of a Circle is Known?

If the radius of a circle is given, then it is easy to determine the diameter formula because we know that the value of diameter is twice the radius. This means that the Diameter formula = 2r.

### What is the Diameter Formula When the Circumference of a Circle is Known?

If the circumference of a circle is given, then it is easy to derive the diameter formula. We know that the formula for the circumference of a circle is Circumference, C = 2πr. We also know that the relationship between the radius and diameter of a circle is Diameter = 2r.

so, if we replace '2r' with 'd' in the existing formula, we get the formula for diameter = Circumference/π

### How to Find Circumference With Diameter Formula?

If the diameter of a circle is given, then we can find the circumference of a circle using the following method. The formula for diameter = Circumference/π. This can also be written as Circumference = πd and the circumference can be calculated.

### How to Find Radius from Diameter Formula?

If the diameter of a circle is given, then the radius can be calculated because we know that the value of the diameter is twice the radius. In other words, the value of radius is half the value of the diameter. This can be written as Radius = Diameter ÷ 2.

### How to Find the Area of a Circle With the Diameter Formula?

The area of a circle can be calculated using the diameter formula. We know that the area of a circle = πr^{2}. Now, we know that Radius = Diameter ÷ 2. So, we can replace the radius (r) with d/2 in the existing formula, area of a circle = πr^{2}. This will make it ,area of a circle = π × (d/2)^{2} or π × (d^{2}/2)^{2} which is area of a circle = πd^{2}/4.

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