This question is not easy to answer and even more complicated to understand. If you imagine any point on a flat surface and a series of points whose distance from that point is identical, then you are looking at a circle.

This question is not easy to answer and even more complicated to understand. If you imagine any point on a flat surface and a series of points whose distance from that point is identical, then you are looking at a circle.

\( r=11 \)

Calculate the circumference.

The perimeter of any circumference can be calculated. Generally, we can say that to calculate it, we must multiply by $2$ the value of $π$ (pi) and the length of the radius.

Click to access the article on the perimeter of the circumference.

Another equally important data that we can obtain with respect to any circumference is the area of the circle. To find it, we must raise the length of the radius squared and then multiply the result obtained by π. Click here to access the article on the area of the circle.

Test your knowledge

Question 1

\( r=7 \)

Calculate the circumference.

Question 2

\( r=2 \)

Calculate the circumference.

Question 3

\( r=6 \)

Calculate the circumference.

**Let's consider the following circle.**

The radius of the circle is equal to $7 cm$.

**Use the image and the data provided to calculate:**

1. the diameter of the circumference

2. the perimeter of the circle

3. the area of the circle

**Solution:**

$P=2\times R\timesπ=2\times7\times3,14=43,96$

The perimeter of the circumference equals $43,96 cm$.

3. To calculate the area of the space inside the circumference, i.e., the circle, we must square the length of the radius of the circumference and then multiply the result obtained by the value of $π$.

**Thus, we obtain:**

$S=π\times R\times R=3,14X7\times7=153,86$

The area of the circle is $153,86cm²$

**Answer:**

The diameter of the circle equals $14 cm$.

Let's consider the following circle.

We know that its diameter is $20cm$.

**Use the image and the data provided to calculate:**

- the radius of the circle
- the perimeter of the circle
- the area of the circle

**Solution:**

- The diameter of the circumference is actually the length of the radius multiplied by $2$. In our case, we already know what the diameter is, so all we have to do to find the length of the radius is to divide the diameter by $2$. By dividing it, we get that the radius of the circumference equals $10 cm$ $(20/2)$ .
- As we have already said, to calculate the perimeter of the circumference we must multiply the value of $π$ l the length of the radius by $2$ (or use the value of the diameter directly instead of multiplying the length of the radius by $2$). The value of $π$ is $3,14$.

**We obtain that:**

$P=2\times R\timesπ=2\times10\times3,14=62,8$

The perimeter of the circumference is $62,8 cm$.To calculate the area of the circle, we must raise the length of the radius (obtained in a. above) of the circumference to the square and then multiply the result obtained by the value of $π$.

**Thus, we obtain:**

$S=π\times R\times R=3,14\times10\times10=314$

- The area of the circle is $314 cm²$.

Do you know what the answer is?

Question 1

A circle has a radius of 3 cm.

What is its perimeter?

Question 2

O is the center of the circle in the diagram.

What is its perimeter?

Question 3

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

What is its circumference?

**Assignment:**

Given the circumference of the figure

The diameter of the circle is $13$,

**Solution**

It is known that the diameter of the circle is twice its radius, i.e. it is possible to know the radius of the circle in the figure.

$13:2=6.5$

**To**find the area of the circle, we replace the data we have in the formula for the calculation of the circle

$A=\pi\times R²$

**We replace the data we have:**

$A=\pi\times6.5²$

$A=\pi42.25$

**Answer**

$pi42.25$

**Request**

Given an equilateral triangle in a circle

What is the areaof the circle?

**Solution**

Recall first the theorem that a circumferential angle that is inclined about the diameter is equal to 90 degrees.

That is, the triangle inside the circle is a right triangle and isosceles, so we can use the Pythagorean formula.

We replace the data we have with the Pythagorean formula

$X=Diámetro$

$(\sqrt{2})²+(\sqrt{2})²=X²$

The root cancels the power and therefore we obtain that

$2+2=X²$

That is

$X²=4$

The root of $4$ is $2$ and therefore the diameter is equal to $2$ and the radius is equal to half of the diameter and therefore it is equal to $1$

Therefore we obtain that the diameter is equal to $2$

And the radius is $1$

Then we add the formula for the area of the circle

**Answer**

$π$

Check your understanding

Question 1

Calculate the area of a circle with a radius of 5 cm.

Question 2

A circle has a radius of 3 cm.

What is its area?

Question 3

A circle has a radius of 6 cm.

What is its area?

**Given the semicircle:**

**Consigna**

Calculate its area

**Solution**

Since we know that it is a semicircle we can conclude that the base of the semicircle is the diameter.

We know that the diameter is twice the radius and therefore we can know the radius of the circle.

$Diámetro = 14$

$14:2=7$

$Radio = 7$

The formula for calculating the area of the circumference is

$A=\pi\times R²$

We replace the data in the formula

$A=\pi\times 7²$

$A=\pi\times 49$

Since the formula was the area of the semicircle we divide the area of the circle by $2$ and get the answer.

$\pi49:2=24.5\pi$

**Answer**

$\pi49:2=24.5\pi$

**Request**

Given the circumference of the figure

Given that the radius is equal to $6$,

What is the circumference?

**Solution**

The radius of the circle is $r=6$

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

Replace by $r=6$

We obtain

$2\cdot\pi\cdot6$

$12\pi$

**Answer**

$12\pi$

Do you think you will be able to solve it?

Question 1

A circle has a radius of 8 cm.

Calculate the area of the circle.

Question 2

A circle has a radius of 10 cm.

Calculate the area of the circle.

Question 3

A circle has a diameter of 14 cm.

Calculate the area of the circle.

**Request**

Given the circumference of the figure.

Given that the radius is equal to $\frac{2}{3}$,

What is the circumference?

**Solution**

The radius of the circle $r=\frac{2}{3}$

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

Replace by $r=\frac{2}{3}$

We obtain

$2\cdot\pi\cdot\frac{2}{3}=$

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

**Answer**

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

**Request**

Given the circumference of the figure.

Given that the radius is equal to $5$,

What is the circumference?

**Solution**

Diameter of the circumference

$2r=5$

We divide by $2$

$r=\frac{5}{2}=2\frac{1}{2}$

Therefore the radius of the circle is $r=2\frac{1}{2}$

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

Replace by $r=2\frac{1}{2}$

We obtain

$2\cdot\pi\cdot2\frac{1}{2}=$

$2\cdot2\frac{1}{2}\cdot\pi=$

$5\pi$

**Answer**

$5\pi$

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

- The center of the circumference
- Radius
- Diameter
- Pi
- The perimeter of the circumference
- Circular area
- Arcs in a circle
- Chords in a circle
- Central angle in a circle
- Perpendicular to the chord from the center of the circle
- Inscribed angle in a circle

**On the** **Tutorela**** blog you will find a variety of articles about mathematics**.

Test your knowledge

Question 1

O is the center of the circle.

AB = 15

Is it possible to work out its circumference?

Question 2

Look at the circle in the figure.

Is it possible to calculate its circumference?

Question 3

\( r=11 \)

Calculate the circumference.

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

What is its circumference?

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

Look at the circle in the figure:

Its radius is equal to 4.

What is its circumference?

The formula for the circumference is equal to:

$2\pi r$

8π

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π7²

π49

49π

Given the circle whose diameter is 7 cm

What is your area?

First, let's remember the formula for the area of a circle:

$\pi r^2$

In the question, we are given the diameter of the circle, but we need the radius.

It is known that the radius is actually half of the diameter, therefore:

$r=7:2=3.5$

We replace in the formula

$\pi3.5^2=12.25\pi$

$12.25\pi$ cm².

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

What is its area?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π3²

π9

$9\pi$ cm²

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- Area
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- Parallelogram
- The area of a parallelogram: what is it and how is it calculated?
- Perimeter of a Parallelogram
- Elements of the circumference
- Circle
- Diameter
- Pi
- Area of a circle
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- Chords of a Circle
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- The perimeter of the rectangle
- Perimeter
- Triangle
- The Area of a Triangle
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- Area of a Scalene Triangle
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