Some of you may know the radius as "dial". Either way, the meaning is identical with the same characteristics. So, what is the radius? It is a specific segment that connects the center of a circle with a particular point on the circumference of it.
Some of you may know the radius as "dial". Either way, the meaning is identical with the same characteristics. So, what is the radius? It is a specific segment that connects the center of a circle with a particular point on the circumference of it.
The formula for calculating the perimeter or circumference of a circle is:
Where is the perimeter of the circle, is the radius of the circle, and is a number approximately equal to .
Given: A circle with a circumference of . The radius of the circle needs to be calculated.
We will place the known data into the formula:
The perimeter can be translated in terms of , that is:
Then we obtain:
Reduce the value of and get . Continue with a division by to isolate the value of .
That is: and, therefore, the result obtained is that the radius of the circle .
A circle has a radius of 3 cm.
What is its perimeter?
More examples:
Given: A circle whose perimeter is , we must calculate the radius of the circle
We will place the data we know into the formula:
The circumference can be translated in terms of , that is:
Then we obtain:
To isolate the value of divide
Therefore, the result is that the radius of the circle
Given a circle with a circumference of , we must calculate the radius of the circle
We will place the known data into the formula:
The circumference can be expressed in terms of , that is:
Then we obtain:
To isolate the value of , it is necessary to divide
Therefore, the result is that the radius of the circle
The data of a circle whose circumference is , the radius of the circle must be calculated.
To isolate the value of divide
Therefore, the result is that the radius of the circle
O is the center of the circle in the diagram.
What is its perimeter?
O is the center of the circle in the figure below.
What is its circumference?
O is the center of the circle.
AB = 15
Is it possible to work out its circumference?
Exercise 1:
Task:
How will the circumference change if we double its diameter?
Solution:
The radius is equal to
The radius is equal to
Answer:
The circumference will double
Exercise 2:
Given the shape of the figure.
The quadrilateral is a square with cm side length.
Task:
What is the perimeter of the figure?
Solution:
The perimeter is made up of halves of the circle.
That is, a total of circumferences with cm diameter.
Circle diameter cm
Answer:
Exercise 3:
Given:
Mirta runs at a speed of minutes per kilometer.
She runs on a circular path with a radius of meters and circles it times.
Task:
How long will Mirta run?
Solution:
First, we calculate the length of the path.
Path length = The circumference has a radius of meters.
Mirta's path distance = Path length = (meters)
That is: km
Answer:
It will take Mirta minutes to complete the run.
Exercise 4:
Given the circle with a circumference of
Question:
What is its area?
Solution:
Let's recall the circumference formula:
We replace with the known data:
We divide by
Now we divide by
From here we can replace the data in the area formula of the circumference:
Answer:
O is the center of the circle in the figure below.
What is its circumference?
We use the formula:
We replace the data in the formula:
cm
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On the Tutorela blog, you'll find a variety of articles about mathematics.
Are you having trouble answering questions where you need to calculate the radius using the perimeter? A private tutor can help you. The role of the tutor is not only to teach you, but also to understand the reasons why you are having difficulties with a particular topic. For example:
In this way, the teacher not only teaches you but also works with you on strengthening weak areas (memorizing formulas, assimilating features of certain shapes, and more...).
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Look at the circle in the figure.
Is it possible to calculate its circumference?
Look at the circle in the figure below.
The radius of the circle equals 5.
What is its perimeter?
Look at the circle in the figure below.
The radius of the circle equals 7.
What is its perimeter?
More and more students are lamenting the way they are taught the material, but they are not explained how to study for exams. There is a big difference between solving a question in class with the teacher and with the help of classmates, and dealing with questions in real time during the exam. The secret to success? Practice the material and mentally prepare to believe in yourself, and above all, reduce feelings of stress. So, how do you prepare for the exam in the best way?
1. Start studying about a week and a half before the exam
Some schools distribute the exam schedule to students on the first day of classes. This means that you know when you will be tested, so you can prepare in advance according to your own time and priorities. A week and a half is a sufficient amount of time to study for a math exam, assuming that you have mastered most of the material and need this period just for practice and memorizing formulas.
2. Create a detailed personal learning program.
Additionally, it's worth creating a schedule for yourself that details what you will study each day of the week. It's not enough to say: "On Monday, I will study circles and radii", but you should specify exactly what you are doing:
3. Breaks during learning are very important
When creating a learning schedule for yourself, also incorporate breaks. If you study for hours on end and intensely, you can reach burnout quickly. The goal is to maintain your motivation and not to arrive at a pre-exam situation of exhaustion. For every two hours of study, take a fresh half-hour break.
4. Blessed Learning Groups!
Is it worth studying with friends? Yes! Just make sure that you're actually studying and it's not turning into an impromptu party. Every three days of study, use a study group with 2-3 members. The goal is to solve exercises together, while each of you can contribute your knowledge to the other members and thus strengthen certain topics. Those of you who want to simulate an exam situation can open timers and check how much time it takes to solve the exercises.
5. Come to math class with questions.
During home study, it's likely that some more challenging and complex questions will arise, which is fine. Teachers allow you to raise questions that you want them to solve in class, and it's definitely worth asking questions. Your teacher will guide you through solving the question, while you will learn how to deal with questions at this specific level during the test.
And what about a private tutor? A personalized math class can definitely contribute to your understanding. The recommendation is not to wait for private lessons only just before the exam, but to make sure you gradually assimilate the material learned throughout your studies. The private lesson can be conducted at the student's home, at the teacher's home, or online.
Look at the circle in the figure below.
The radius of the circle is equal to 8.
What is its perimeter?
Look at the circle in the figure below.
The diameter of the circle is 4.
What is its perimeter?
Look at the circle in the figure.
The diameter of the circle is 10.
What is its perimeter?