Elements of the circumference

🏆Practice circle

What is circumference?

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.

B - What is circumference

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Test yourself on circle!

einstein

\( r=2 \)

Calculate the circumference.

222

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Circumference characteristics

Circumference perimeter

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

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

B - perimeter of the circumference


Circle area

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.

Area = π×r²


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Examples and practice

Exercise 1

Let's consider the following circle.

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

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×R×π=2×7×3,14=43,96 P=2\times R\timesπ=2\times7\times3,14=43,96

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

Thus, we obtain:

S=π×R×R=3,14X7×7=153,86 S=π\times R\times R=3,14X7\times7=153,86

The area of the circle is 153,86cm2 153,86cm²

Answer:

The diameter of the circle equals 14cm 14 cm .


Exercise 2

Let's consider the following circle.

We know that its diameter is 20cm20cm .

diameter is 20 cm

Use the image and the data provided to calculate:

  1. the radius of the circle
  2. the perimeter of the circle
  3. the area of the circle

Solution:

  1. The diameter of the circumference is actually the length of the radius multiplied by 2 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 2 . By dividing it, we get that the radius of the circumference equals 10cm 10 cm (20/2) (20/2) .
  2. As we have already said, to calculate the perimeter of the circumference we must multiply the value of π π l the length of the radius by 2 2 (or use the value of the diameter directly instead of multiplying the length of the radius by 2 2 ). The value of π π is 3,14 3,14 .

We obtain that:

P=2×R×π=2×10×3,14=62,8 P=2\times R\timesπ=2\times10\times3,14=62,8

The perimeter of the circumference is 62,8cm 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 π .

Thus, we obtain:

S=π×R×R=3,14×10×10=314 S=π\times R\times R=3,14\times10\times10=314

  1. The area of the circle is 314cm2 314 cm² .

Do you know what the answer is?

Circumference exercises:

Exercise 1

Assignment:

Given the circumference of the figure

The diameter of the circle is 13 13 ,

What is its area?

Exercise 1 Assignment Given the circumference of the figure

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 13:2=6.5

Tofind the area of the circle, we replace the data we have in the formula for the calculation of the circle

A=π×R2 A=\pi\times R²

We replace the data we have:

A=π×6.52 A=\pi\times6.5²

A=π42.25 A=\pi42.25

Answer

pi42.25 pi42.25


Exercise 2

Request

Given an equilateral triangle in a circle

What is the areaof the circle?

Exercise 2 Assignment Given an equilateral triangle in a 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=Diaˊmetro X=Diámetro

(2)2+(2)2=X2 (\sqrt{2})²+(\sqrt{2})²=X²

The root cancels the power and therefore we obtain that

2+2=X2 2+2=X²

That is

X2=4 X²=4

The root of 44 is 22 and therefore the diameter is equal to 22 and the radius is equal to half of the diameter and therefore it is equal to 11

Therefore we obtain that the diameter is equal to 22

And the radius is 1 1

Then we add the formula for the area of the circle

Answer

π π


Check your understanding

Exercise 3

Given the semicircle:

new Exercise 3- Given the semi-circle

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.

Diaˊmetro=14 Diámetro = 14

14:2=7 14:2=7

Radio=7 Radio = 7

The formula for calculating the area of the circumference is

A=π×R2 A=\pi\times R²

We replace the data in the formula

A=π×72 A=\pi\times 7²

A=π×49 A=\pi\times 49

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

π49:2=24.5π \pi49:2=24.5\pi

Answer

π49:2=24.5π \pi49:2=24.5\pi


Exercise 4

Request

Given the circumference of the figure

Given that the radius is equal to 6 6 ,

What is the circumference?

Exercise 4- Assignment Given the circumference of the figure

Solution

The radius of the circle is r=6 r=6

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

Replace by r=6 r=6

We obtain

2π6 2\cdot\pi\cdot6

12π 12\pi

Answer

12π 12\pi


Do you think you will be able to solve it?

Exercise 5

Request

Given the circumference of the figure.

Given that the radius is equal to 23\frac{2}{3},

What is the circumference?

Exercise 5- Assignment Given the circumference in the figure

Solution

The radius of the circle r=23 r=\frac{2}{3}

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

Replace by r=23 r=\frac{2}{3}

We obtain

2π23= 2\cdot\pi\cdot\frac{2}{3}=

43π \frac{4}{3}\pi

Answer

43π \frac{4}{3}\pi


Exercise 6

Request

Given the circumference of the figure.

Given that the radius is equal to 5 5 ,

What is the circumference?

Given that the radius is equal to 5 What is the circumference

Solution

Diameter of the circumference

2r=5 2r=5

We divide by 2 2

r=52=212 r=\frac{5}{2}=2\frac{1}{2}

Therefore the radius of the circle is r=212 r=2\frac{1}{2}

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

Replace by r=212 r=2\frac{1}{2}

We obtain

2π212= 2\cdot\pi\cdot2\frac{1}{2}=

2212π= 2\cdot2\frac{1}{2}\cdot\pi=

5π 5\pi

Answer

5π 5\pi


Test your knowledge

examples with solutions for circle

Exercise #1

Given the circle whose diameter is 7 cm

What is your area?

777

Video Solution

Step-by-Step Solution

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

 πr2 \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 r=7:2=3.5

We replace in the formula

π3.52=12.25π \pi3.5^2=12.25\pi

Answer

12.25π 12.25\pi cm².

Exercise #2

Look at the circle in the figure.

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

6

Video Solution

Step-by-Step Solution

Formula of the circumference:

P=2πr P=2\pi r

We replace the data in the formula:

P=2×6×π P=2\times6\times\pi

P=12π P=12\pi

Answer

12π 12\pi

Exercise #3

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

What is its area?

333OOO

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π3²

π9

 

Answer

9π 9\pi cm²

Exercise #4

Look at the circle in the figure:

777

The radius is equal to 7.

What is the area of the circle?

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π7²

π49

Answer

49π

Exercise #5

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Video Solution

Step-by-Step Solution

The formula for the circumference is equal to:

2πr 2\pi r

Answer

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