The circumference is actually the length of the circular line. It is calculated by multiplying the radius by 2, which has an approximate value of π. It can also be said that the circumference is equal to the the diameter of the circumference multiplied by π (since the diameter is actually twice the radius of the circumference). It is customary to identify the circumference (the perimeter) with the letter P.

The formula for calculating the circumference is:

$P=2\times\pi\times R$

We will illustrate the concept with a simple example. Here is a circle, as shown in the drawing in front of you:

The radius of the circumference is $3\text{ cm}$.

You can calculate the circumference of the circle by placing the data:

We know the diameter of the circle, to calculate its circumference we must find the radius.

The diameter of the circle is twice the radius, so we can conclude that half of the diameter is the radius:

$12:2=R=6$

We put the result in the formula to calculate the circumference of the circle and we will get the answer:

$P=2\times\pi\times R$

$P=2\times3.14\times6=37.68$

Answer

$12\pi$ or $37.68$ cm

Exercise 9

Task

A bicycle has tires with a radius of $40$ cm,

the wheels made five complete turns.

How far did the bicycle travel?

Solution

First we calculate the circumference of the wheels of the bicycle.

We know that the radius is $40$ cm, so we will put the radius in the formula to calculate the circumference.

$P=2\times\pi\times R$

$P=2\times3.14\times40$

$P=2\times3.14\times40=251.2$

Now that we know that the circumference of the wheels is $251.2$ cm, we can calculate the distance they traveled by multiplying the circumference by the number of turns:

$5\times251.2=1256$

Since we want to know the distance in meters we will divide it by $100$

For a scientific experiment, Sebastian needs to produce a wheel that turns exactly $17$ times around a track $6.8$ m long.

What should the radius of the wheel be?

Solution

To solve, let's first understand the question.

For the wheel to make $17$ turns in a distance of $6.8$ mts, the circumference must be equal to:

$\frac{680}{17}=40$

That is, the circumference is equal to $40$

The question is what is the radius of the circle and therefore we put the data we have in the formula for calculating the circumference.

$P=2\times\pi\times R$

$40=2\times3.14\times R$

$2\times3.14=6.28$

$40=6.28R$

$\frac{40}{6.28}=R$

$R=6.36$

Answer:

$R=6.36$ meters.

Review questions

What is the circumference?

As we know, the perimeter of a figure length of all of the sides of that figure, in the case of the circle its perimeter, called the circumference, is the measure or length of the entire circular line.

How to measure the circumferenceof a circle?

To calculate the circumference we have two formulas that we can use:

$P=2\pi r$

Where

$P$ is the perimeter

$\pi=3.14$

$r$ is the radius

By definition we know that the radius is half the diameter or the diameter is twice the radius, then according to what $D=2r$, we can use the following formula

$P=\pi D$

What is an example of finding the circumference?

Example

Calculate the circumference of the circle, given that $r=5\text{ cm}$

Solution:

To calculate the circumference, we will use that the radius $r=5\text{ cm}$ and just substitute in our formula:

$P=2\pi r$

$P=2\times3.14\times5\operatorname{cm}$

$P=6.28\times5\operatorname{cm}$

$P=31.4\operatorname{cm}$

Ó

$P=2\times\pi\times5\operatorname{cm}$

$P=10\pi\text{ cm}$

Solution

$P=10\pi\text{ cm}$

Ó

$P=31.4\operatorname{cm}$

Do you know what the answer is?

Question 1

Given the circle whose radius has a length of 9 cm