Some of you may know the radius as a "dial". Either way, the meaning is identical with the same characteristics. So, what is the radius? It is a specific segment that connects the center of a circle with a particular point on the circumference .

## How is the radius calculated using its perimeter?

The formula for calculating the perimeter or circumference of a circle is: $P=2πR$

Where $P =$ is the perimeter of the circle, $R =$ is the radius of the circle, and $π =$ is a number approximately equal to $3.14$.

Given: A circle with a circumference of $18.84$. The radius of the circle needs to be calculated.

We will place the known data into the formula: $18.84=2πR$

The perimeter can be translated in terms of $π$, that is: $18.84:3.14=6$

Then we obtain: $6π=2πR$

Reduce the value of $π$ and get $6=2R$. Continue with a division by $2$ to isolate the value of $R$.

That is: $R=\frac{6}{2}$ and, therefore, the result obtained is that the radius of the circle $=3$.

## Examples with solutions for How is the radius calculated using its circumference?

### Exercise #1

Look at the circle in the figure:

Its radius is equal to 4.

What is its circumference?

### Step-by-Step Solution

The formula for the circumference is equal to:

$2\pi r$

### Exercise #2

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

### Step-by-Step Solution

Formula of the circumference:

$P=2\pi r$

We insert the given data into the formula:

$P=2\times6\times\pi$

$P=12\pi$

$12\pi$

### Exercise #3

O is the center of the circle in the figure below.

What is its circumference?

### Step-by-Step Solution

We use the formula:$P=2\pi r$

We replace the data in the formula:$P=2\times8\pi$

$P=16\pi$

$16\pi$ cm

### Exercise #4

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

### Step-by-Step Solution

To calculate, we will use the formula:

$\frac{P}{2r}=\pi$

Pi is the ratio between the circumference of the circle and the diameter of the circle.

The diameter is equal to 2 radii.

Let's substitute the given data into the formula:

$\frac{8}{4}=\pi$

$2\ne\pi$

Therefore, this situation is not possible.

Impossible

### Exercise #5

Look at the circle in the figure.

The radius of the circle is $\frac{2}{3}$.

What is its perimeter?

### Step-by-Step Solution

The radius is a straight line that extends from the center of the circle to its outer edge.

The radius is essential for calculating the circumference of the circle, according to the following formula:

If we substitute the radius we currently have, the formula will be:

2*π*2/3

Let's start solving, we'll rearrange the formula:

π*2*2/3 =

We'll multiply the fraction by the whole number:

π*(2*2)/3 =

π*4/3 =

4/3π

And that's the result!

$\frac{4}{3}\pi$

### Exercise #6

A circle has a circumference of 31.41.

### Step-by-Step Solution

To solve the exercise, first we must remember the circumference formula:

$P= 2\pi R$

P is the circumference and Pi has a value of 3.14 (approximately).

We substitute in the known data:

$31.41=2\cdot3.141\cdot R$

Keep in mind that the result can be easily simplified using Pi:

$\frac{31.41}{3.141}=2R$

$10=2R$

Finally, we simplify by 2:

$5=R$

5

### Exercise #7

A circle has a circumference of 50.25.

### Step-by-Step Solution

We use the formula:

$P=2\pi r$

We insert the known data into the formula:

$50.25=3.14\times2r$

$50.25=2\times r\times3.14$

$50.25=6.28r$

$\frac{50.25}{6.28}=\frac{6.28r}{6.28}$

$r=8$

8

### Exercise #8

The circumference of a circle is 14.

How long is the circle's radius?

### Step-by-Step Solution

We begin by using the formula:

$P=2\pi r$

We then insert the given data into the formula:

$14=2\times\pi\times r$

Lastly we divide Pi by 2:

$\frac{14}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{7}{\pi}=r$

$\frac{7}{\pi}$

### Exercise #9

Below is a circle bounded by a parallelogram:

All meeting points are tangential to the circle.
The circumference is 25.13.

What is the area of the parallelogram?

### Step-by-Step Solution

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

$AE=AF=3$
$BG=BF=6$

And from here we can calculate:

$AB=AF+FB=3+6=9$

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

Since the circumference is 25.13.

Circumference formula:$2\pi R$
We replace and solve:

$2\pi R=25.13$
$\pi R=12.565$
$R\approx4$

The height of the parallelogram is equal to two radii, that is, 8.

And from here you can calculate with a parallelogram area formula:

$AlturaXLado$

$9\times8\approx72$

$\approx72$

### Exercise #10

The area of the rectangle in the drawing is 28X cm².

What is the area of the circle?

### Step-by-Step Solution

Let's draw the center of the circle and we can divide the diameter of the circle into two equal radii

Now let's calculate the length of the radii as follows:

$7\times2r=28x$

$14r=28x$

We'll divide both sides by 14:

$r=\frac{28}{14}x$

$r=2x$

Let's calculate the circumference of the circle:

$P=2\pi\times r=2\pi\times2x=4\pi x$

$4\pi x$

### Exercise #11

The following is a circle enclosed in a parallelogram:

All meeting points are tangent to the circle.
The circumference is 25.13.

What is the area of the zones marked in blue?

### Step-by-Step Solution

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

$AE=AF=3$
$BG=BF=6$

From here we can calculate:

$AB=AF+FB=3+6=9$

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

It is known that the circumference of the circle is 25.13.

Formula of the circumference:$2\pi R$
We replace and solve:

$2\pi R=25.13$
$\pi R=12.565$
$R\approx4$

The height of the parallelogram is equal to two radii, that is, 8.

And from here it is possible to calculate the area of the parallelogram:

$\text{Lado }x\text{ Altura}$$9\times8\approx72$

Now, we calculate the area of the circle according to the formula:$\pi R^2$

$\pi4^2=50.26$

Now, subtract the area of the circle from the surface of the trapezoid to get the answer:

$72-56.24\approx21.73$

$\approx21.73$

### Exercise #12

$r=2$

Calculate the circumference.

12.56

### Exercise #13

Given the circle whose radius has a length of 9 cm

What is its perimeter?

56.55

### Exercise #14

$r=6$

Calculate the circumference.

37.699

### Exercise #15

$r=7$

Calculate the circumference.