**Pi is a mathematical value, approximately equal to** **$3.14$****. This is the commonly used approximation for calculations.**

Pi is symbolized by $π$.

**Examples of some mathematical expressions include** **$π$****:**

$P_○=2\times R\timesπ$

$A_○=π\times R\times R$

**Pi is a mathematical value, approximately equal to** **$3.14$****. This is the commonly used approximation for calculations.**

Pi is symbolized by $π$.

**Examples of some mathematical expressions include** **$π$****:**

$P_○=2\times R\timesπ$

$A_○=π\times R\times R$

There are only 4 radii in 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
- The perimeter of the circle
- 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** **Tutorela**** website you will find a variety of articles on mathematics**.

**What does the number Pi represent?**

Pi is a number that represents the constant relationship between the circumference and its diameter.

**What is the value of the number Pi?**

The value of Pi is approximately $3.14$ and its decimal representation includes an infinite number of digits.

**What are the characteristics of the number Pi?**

Pi is a pure number, and it is also irrational.

**Expression of the number "Pi" as a fraction?**

The fraction of Pi is $\frac{22}{7}$ (approximately).

**Problem**

Given the deltoid $ABCD$ and the circle whose center $O$ is on the diagonal $BC$

The area of the deltoid is $28\operatorname{cm}²$

$AD=4$

What is the area of the circle?

**Solution**

Area of the deltoid $ABCD$

$28=\frac{AD\cdot CB}{2}=2CB$

Divided by $2$

$14=CB$

The diameter of the circle is $CB$

Diameter times half is equal to radius

Replace accordingly

$\frac{1}{2}\cdot14=7$

$A=\pi r^2=\pi\cdot7^2$

$A=49\pi$

**Answer**

$49\pi$

Test your knowledge

Question 1

If the radius of a circle is 0.5 cm, then the length of the diameter is 10 cm.

Question 2

The number Pi \( (\pi) \) represents the relationship between which parts of the circle?

Question 3

M is the center of the circle.

In the figure we observe 3 diameters?

**Question**

Given the parts of the circle shown in the figure (white)

Diameter of the circle $11\operatorname{cm}$

How much is the area of the shaded parts together?

The area of the parts is like the area of the circle minus the two sections, one of which extends by an angle of $30°$ and the other by an angle of $15°$

**In the same way we can look at the parts like this:**

Then its area is the area of the circle minus the area of the section extended by an angle of $(45°)$

Or it is just a cut area extending by $(360°)$ degrees minus $(45°)$ degrees, i.e.,$(315°)$ degrees.

$A=\frac{315°}{360°}\cdot\pi\cdot(\frac{11}{2})^2=83.11$

**Answer**

$83.11\operatorname{cm}²$

**Question**

What is the area of a slice of pizza whose diameter is $45\operatorname{cm}$ after dividing into $8$ slices?

**Solution**

Pizza divided by: $8$ slices

In other words, the area of a slice of pizza is $\frac{1}{8}$

$Apizza=\pi\cdot r²=\pi\cdot(\frac{diámetropizza}{2})²$

$\pi\cdot(\frac{45}{2})^2=506.25\pi$

$A=\frac{1}{8}\cdot506.25\pi$

$198.7\operatorname{cm}²$

**Answer**

$198.7\operatorname{cm}²$

Do you know what the answer is?

Question 1

Is there sufficient data to determine that

\( GH=AB \)

Question 2

M is the center of the circle.

Perhaps \( MF=MC \)

Question 3

M is the center of the circle.

Perhaps \( AB=CD \)

**Problem**

Given the circumference that at its center $O$

Is it possible to calculate its area?

**Solution**

The center of the circle is $O$

That is, the given line is the diameter.

Diameter = Radius multiplied by 2

$2r=10$

$r=5$

We use the formula for calculating the area

$S=\pi r^2=$

$\pi5^2=25\pi$

**Answer**

Yes, its area is $25\pi$

**Question**

Given the circle in the figure. $AB$ is the chord.

Is it possible to calculate the area of the circle?

**Solution**

We know nothing about $AB$ other than that it is a chord we have not been given the diameter or radius, therefore it is not possible to calculate the area.

**Answer**

It is not possible to calculate the area

Check your understanding

Question 1

Which diagram shows a circle with a point marked in the circle and not on the circle?

Question 2

Which figure shows the radius of a circle?

Question 3

Is it correct to say the area of the circumference?

The number pi is the number of times the diameter fits in the entire circumference, in this case it fits $3.14159265358$, which is the value of $\pi$.

Different mathematicians studied the relationship between the diameter and the circumference or perimeter. Then they studied that the diameter fits $3.1415$ times in the whole circumference approximately. The way to obtain the value of pi is with the following formula:

$\frac{\text{circunferencia}}{diámetro}=\pi$

Do you think you will be able to solve it?

Question 1

All ____ about the circle located in the distance ____ from the ____ circle

Question 2

In which of the circles is the center of the circle marked?

Question 3

A chord is a segment that connects two points on a circle.

The approximate value of pi is $3.14159265358$, but to use it only 2 or 4 decimal places are enough, that is to say we can take $\pi=3.14$ or $\pi=3.1416$ if we round it up.

The number pi has an infinite number of decimal places and that is why it is considered an irrational number, but among studies of pi, 10 to 15 decimal places are usually used.

Test your knowledge

Question 1

The diameter of a circle is twice as long as its radius.

Question 2

A circle has infinite diameters.

Question 3

There are only 4 radii in a circle.

There are only 4 radii in a circle.

A radius is a straight line that connects the center of the circle with a point on the circle itself.

Therefore, the answer is incorrect, as there are infinite radii.

False

Which figure shows the radius of a circle?

It is a straight line connecting the center of the circle to a point located on the circle itself.

Therefore, the diagram that fits the definition is c.

In diagram a, the line does not pass through the center, and in diagram b, it is a diameter.

Which diagram shows a circle with a point marked in the circle and not on the circle?

The interpretation of "in a circle" is inside the circle.

In diagrams a'-d' the point is on the circle, and in diagram c' the point is outside the circle.

M is the center of the circle.

Perhaps $AB=CD$

CD is a diameter, since it passes through the center of the circle, meaning it is the longest segment in the circle.

AB does not pass through the center of the circle and is not a diameter, therefore it is necessarily shorter.

Therefore:

$AB\ne CD$

No

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

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

Related Subjects

- Area
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- Area of a trapezoid
- Perimeter of a trapezoid
- Parallelogram
- The area of a parallelogram: what is it and how is it calculated?
- Perimeter of a Parallelogram
- Elements of the circumference
- Circle
- Area of a circle
- Distance from a chord to the center of a circle
- Chords of a Circle
- Central Angle in a Circle
- Arcs in a Circle
- Perpendicular to a chord from the center of a circle
- Inscribed angle in a circle
- Tangent to a circle
- The Circumference of a Circle
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- The perimeter of the rectangle
- Perimeter
- Triangle
- The Area of a Triangle
- Area of a right triangle
- Area of Isosceles Triangles
- Area of a Scalene Triangle
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