The Circumference of a Circle

If this article interests you, you may also be interested in the following articles:

• The circumference
• The center of the circumference
• Circle
• Radius
• Diameter
• Pi
• Circular area
• Arcs in a circle

In Tutorela you will find a variety of articles about mathematics.

Task

Given the circle whose radius $3\operatorname{cm}$

What is its circumference?

Solution

We use the formula of the circumference $2\pi r$

Replace the given radius accordingly

$p=2\pi\cdot3=6\pi$

Answer

$6\pi$

Task

Given the circle in the figure

What is its diameter?

Solution

We use the formula of the circumference $2\pi r$

Replace the data accordingly

$16\pi=2\pi\cdot r$

Divide by $2\pi$

$\frac{16\pi}{2\pi}=r$

Reduce by $\pi$

$r=8$

Diameter= Radius multiplied by $2$

$2\cdot8=16$

Answer

$16$

Task

Given the circle in the figure

Is it possible to find the circumference?

Solution

The given chord of the circle is not the diameter or the radius and no other data is given other than the chord in the figure.

It is not possible to calculate a circle without some data about the radius or the diameter or without other information that helps to find them.

Answer

It is not possible to find the circumference

Question

What is the radius of the circle whose circumference is $9a\pi$ cm?

Solution

We use the formula of the circumference $2\pi r$

Replace accordingly

$2\pi r$

Divide by $2\pi$

$\frac{9a\pi}{2\pi}=r$

Reduce by pi

$r=4.5a$

Answer

$4.5a$

Task
Given the shape in the figure

The quadrilateral is a square in which each side is extended by a quarter circle, the quarters of the circle being identical.

Given that the total circumference of the shape is $24+12\pi$ cm.

What are the lengths of the sides of the square?

Solution

The parts marked by R are the radii of the 4 circles.

We calculate the circumference of the shape

The marked sides are part of the circumference

$\left(forma\right)P=4\cdot\frac{1}{4}P\left(círculo\right)+4r\left(círculo\right)$

$\left(forma\right)P=P\left(forma\right)+4R\left(círculo\right)$

$\left(forma\right)P=2\pi R+4R$

$24+12\pi=2\pi R+4R$

$24+12\pi=R(2\pi+4)$

Divide by $2\pi+4$

$\frac{24+12\pi}{2\pi+4}=R$

$\frac{6(2\pi+4)}{2\pi+4}=R$

Divide by $2\pi+4$

$R=6$

Answer

$6$

Task

Given the circle in the figure:

The radius is equal to $4\text{ cm}$

What is its circumference?

Solution

Since we know the radius, all we have to do is replace the data in the formula to calculate the circumference of the circle:

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

$P=2\times3.14\times4=25.12$

Answer

$8\pi$ o $25.12\text{ cm}$

Task

Given the circle whose radius has a length of $9$ cm

What is its circumference?

Solution

Since we know the radius, all we have to do is replace the data in the formula to calculate the circumference of the circle:

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

$P=2\times3.14\times9=56.52$

Answer

$56.52\text{ cm}$

Task

Given the circle whose diameter is $12\text{ cm}$

What is its circumference?

Solution

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

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 $100$

$\frac{1256}{100}=12.56$

Answer

$12.56$ meters

Task

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.

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 circumference of 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

$P=31.4\operatorname{cm}$