How To Calculate Area Of Circle Using Diameter

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The notion of circles and their properties are ubiquitous in the field of mathematics. It is fascinating how a simple geometric shape like a circle can have so many intricate properties. In this article, we will delve into the area of circles and how we can calculate it from the diameter or radius. Before we delve into the nitty-gritty of area calculation, let's brush up on some basic concepts about circles.

What is a Circle?

A circle is a two-dimensional closed shape that consists of points equidistant from a fixed point in a plane. The fixed point is called the "center" of the circle, and the distance from the center to any point on the circle is called the "radius." A line segment that passes through the center and has its endpoints on the circle is called the "diameter."

The most fascinating property of a circle is that it has a constant ratio of the circumference to its diameter, denoted by the symbol 'π' (pi), which is approximately equal to 3.14. That means, no matter the size of the circle, its circumference will always be approximately three times the length of its diameter.

Calculating the Area of a Circle

The area of a circle is defined as the total amount of space enclosed by the circle in a two-dimensional plane. The formula for calculating the area of a circle is:

Area = π x (radius)^2

From this formula, we can see that the area of a circle depends only on the radius of the circle. Given the radius of a circle, one can easily find its area using the above formula. However, sometimes we may not be given the radius directly, but we may be given the diameter. In such cases, we need to convert the diameter into the radius before using the formula for area calculation.

Radius and Diameter Relationship

The relationship between the radius and diameter of a circle is straightforward. The diameter is simply twice the length of the radius. That is:

Diameter = 2 x Radius

Calculating the Area from Diameter

Suppose we are given the diameter of a circle and are required to find its area. In that case, we need to convert the diameter into the radius. The formula for converting diameter to radius is:

Radius = Diameter / 2

Using this formula, we can find the radius of the given circle. Once we have the radius, we can apply the area formula mentioned above to calculate the area.

Example

Let's take an example to understand this better. Suppose we are given the following image of a circle with a diameter of length 14 cm.

To find the area of this circle, we need to convert the diameter into the radius using the formula mentioned earlier:

Radius = Diameter / 2 = 14cm / 2 = 7cm

Now that we have the radius, we can apply the area formula and calculate the area of the circle:

Area = π x (radius)^2 = 3.14 x (7 cm)^2 = 153.86 cm^2

Therefore, the area of the given circle is 153.86 square cm.

Calculating the Area from Radius

When we are given the radius of a circle, we can easily find its area using the area formula mentioned above.

Example

Let's take another example to understand this better. Suppose we are given the following image of a circle with a radius of length 5 cm.

To find the area of this circle, we simply need to apply the area formula:

Area = π x (radius)^2 = 3.14 x (5 cm)^2 = 78.5 cm^2

Therefore, the area of the given circle is 78.5 square cm.

Conclusion

In conclusion, we can say that circles are fascinating shapes with unique properties. The area of a circle, which is defined as the total amount of space enclosed by the circle, depends only on the radius. We can easily calculate the area of a circle using the formula mentioned above. If we are given the diameter of a circle, we can convert it into the radius using a simple formula. On the other hand, if we are given the radius of a circle, we can directly apply the formula for area calculation. With these simple procedures, we can find the area of any circle and explore the beauty of this intriguing shape.


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