The radius is one of the many elements that exist in a circle. The radius is a segment that connects the center of the circle with any point located on the circle itself. Each circle has an infinite number of radii and their length is exactly the same, that is, they are identical.

In this article we will learn what the radius is and we will see how we can use it to calculate the perimeter of the circle and the area of the circle.

The radius is a segment that connects the center of the circle with any point located on the circle itself. We will illustrate it with a graph

Every circle has a center point. In the following illustration it is marked with the letter O. Now we will draw a line from the center point to any other point on the circle.

This line is the radius of the circle, usually denoted by the letter $R$ uppercase or $r$ lowercase. We can draw an infinite number of radii on each circle and they will all be of identical length.

For example, on this circle we have drawn three radii. All the radii of the circle have the same length. That is, the radius of a circle has a fixed length.

Diameter

The diameter of the circumference is the chord that passes exactly through the center and is usually denoted by the letter D.

For example:

The length of the diameter is equal to twice the length of the radius. Can you understand why? We can imagine that the diameter is composed of two radii.

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With the length of the radius we can calculate the perimeter of the circle and the area of the circle. Just for that we have the formulas that will help us to do it.

We will mark the perimeter of the circle with the letter $P$. The formula to calculate the perimeter of the circle is:

$C=2πr$

Let's explain it in words: the circumference equals $2$ multiplied by the number PI, multiplied by the radius. Recall that the value of PI(which is detailed in other articles), is approximately equivalent to $3.14$

Here are some examples:

Example 1

Given a circle, knowing that its radius measures $3$ cm.

What is the perimeter of the circumference?

Solution:

Let's write it down

$R=3$

Now let's remember the formula we just learned to calculate the perimeter:

$P=2πr$

Let's put in the formula the parameters and we will get:

$P=2\times3.14\times3$

$P=18.84$ cm

Thus, we have based on the length of the radius to find the perimeter.

Area of the circle

With the radius we can also calculate the area of the circle, usually denoted by the letter $A$. Just for that we have the following formula:

$A=πr^2$

Let's explain it in words: the area of the circle equals PI times the radius squared.

Do you know what the answer is?

Question 1

Is it correct to say the area of the circumference?

Now let's remember the formula to calculate the area of a circle:

$A=πr^2$

and let's set the parameters.

$A=3.14\times4^2$

$A=3.14\times16$

$A=50.24$

That is, we have arrived at that the area of the circle is $50.24$ cm².

Pay attention to the units of measurement. The length of the radius is given in cm, but it is raised to the power of two and, therefore, the area is measured in cm² (cm squared).

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Recall that the radius of a circle is a line segment that passes from the center of the circle and touches one of the points of the circumference, and is half the diameter. Let's look at the following image to see the radius of the circle.

What is the radius of a circle 10 cm in diameter?

The radius is half of the diameter or we can say that the diameter is twice the radius, therefore if the diameter is equal to $10\text{ cm}$, then half will be the radius and therefore