Understanding the formula for the area of ​​a circle and the formula for the circumference of a circle

The formula for the area of ​​a circle – In mathematics, a circle can be said to be the most different plane figure compared to a number of other shapes. The characteristics, components and also the formula for the area of ​​a circle and also the formula for the circumference of a circle are not the same as most flat shapes.

For this reason, in this article, Sinaumed’s will study the most difficult things about circular shapes, namely the formula for the area of ​​a circle and the formula for the circumference of a circle, accompanied by a number of practice questions so that your understanding of these two topics can get deeper.

Circle Features

Basically, a circle is a plane shape consisting of all points on a plane that are at a certain distance from its center. So, the shape of the sides of this circle can be concluded to be equal and symmetrical from one point to another in this flat shape.

There are several characteristics of a circle that Sinaumed’s should learn first so that you can understand the formula for the area of ​​a circle and the formula for the circumference of a circle which you will learn later. These characteristics will be discussed briefly and formed in points to facilitate understanding.

  1. It doesn’t have any angles.
  2. Even so, the total angle still reaches 360 degrees.
  3. Has no side.
  4. Thus, a circle has an infinite number of fold and rotary symmetries.
  5. The length of the centerline of a circle is called the diameter, while half of the diameter is called the radius.

Circle Area Formula

After studying the characteristics above, Sinaumed’s should be able to learn and understand the formula for the area of ​​a circle that will be presented in this session. You can read and understand the formula for the area of ​​a circle in the image below

In the formula for the area of ​​a circle, Sinaumed’s needs to know that the calculation will involve the element “π” or “phi”. The value of this phi can be 22/7 or 3.14, depending on the question giver. Also, you’ll be using the radius instead of the diameter.

And the rest, the calculation to find the area of ​​this circle is the same as any other flat shape. Sinaumed’s only needs to enter all the components in the problem into the formula. Calculations regarding the area of ​​a circle may be a little more difficult, so it’s a good idea to do it carefully and slowly.

Circle Area Problems Practice

Of course, Sinaumed’s won’t stop after learning the area formula for the environment, right? In mathematics, learning theory alone is not enough. One needs to apply the theory and experiment with what they previously learned.

For that, this time you will try to do a number of problems related to the area of ​​a circle. More specifically, Sinaumed’s will find 3 questions related to this topic, arranged from the easiest to the most difficult to test your understanding.
If you are familiar with the formula for the area of ​​a circle, you may only need to look at the answers to these questions. However, for Sinaumed’s who feel they need help because they don’t really understand this material, we will work on this problem together complete with the steps for doing it.

First Question

A circle has a radius of 10.5 cm. Based on this information, calculate the area of ​​this circle (π = 22/7).
This first problem was made so that Sinaumed’s could directly test the formula for the area of ​​a circle that you previously learned with numbers. So, what you need to do now is quite simple, which is to enter all the components into this circle formula.

L = π x r²
L = 22/7 x 10.5 cm x 10.5 cm
W = 346.5 cm²

When working on problems related to circles, make sure Sinaumed’s uses the π that has been instructed so he can find the right answer. And in this first problem, the area of ​​the circle is 346.5 cm².

Second Problem

It is known that a circle has an area of ​​490.625 cm². What diameter does the circle have? (π = 3.14).
Slightly more complicated than the first question, this second question is made to test your understanding and flexibility regarding variations in questions, in this case, regarding circles. Maybe this second question will make some Sinaumed’s confused about the process.

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However, what you need to remember is that the basic principle of the calculation will remain the same. So, if Sinaumed’s isn’t so sure about doing it, you can try first entering the existing components into the formula and solving it according to the circumstances.

L = π x r²
490.625 cm² = 3.14 x r²
490.625 cm² ÷ 3.14 = r²
156.25 cm² = r²
√156.25 cm = r
12.5 cm = r

Even though you have found the radius of this circle, your journey is still not finished. The last thing Sinaumed’s needs to do is convert those radii into diameters or “d”. Below is how to convert radius to diameter.

d = 2 xr
d = 2 x 12.5 cm
d = 25 cm

With this, Sinaumed’s’ work for the second problem was completed. Even though it is quite long, if you have thoroughness and patience, you will definitely be able to find the answer. So, the diameter for this circle is 25 cm long.

Third Problem

A circle has a diameter of 30 cm. Find the area of ​​the larger circle if calculated using π = 22/7 and π = 3.14 respectively.

For the third and last problem, Sinaumed’s explained earlier that using different π can produce different results. In this matter, we will prove together whether this fact is true or not.

Compared to the second question, there may be some Sinaumed’s who find this question easier. This is because basically, all you need to do is plug in the components of the formula for the area of ​​a circle and look up the final result

.
However, the calculation will be quite long and certainly requires patience and accuracy in the process. This calculation will begin by converting the diameter to the radius first so you can calculate the area of ​​a circle. Here’s how:

r = d ÷ 2
r = 30 cm ÷ 2
r = 15 cm

And after that, Sinaumed’s could try one by one the formula for the area of ​​a circle, each with a different π, namely 22/7 and 3.14. You can immediately try to calculate the area of ​​this circle and prove whether or not the final result will be different.

π = 22/7
L = π x r²
W = 22/7 x 15 cm x 15 cm
W = 707.142 cm²
π = 3.14
W = π x r²
W = 3.14 x 15 cm x 15 cm
D = 706.5 cm²

From the calculations above, it is evident that with a different π, you will also get different results for the area of ​​the circle. In this third problem, it can be concluded that the calculation using π = 22/7 will produce a larger area compared to π = 3.14.

Circle Circumference Formula

After studying the formula for the area of ​​a circle as a whole, this time Sinaumed’s will try to learn the formula for the circumference of a circle. You yourself must have understood that the area formula and the perimeter formula of a flat shape cannot be separated. You can find and learn the formula for the circumference of this circle in the image below.

Like the formula for the area of ​​a circle, the formula for the circumference of a circle also involves the element phi in it. Here, however, Sinaumed’s was able to find that the circumference of a circle required the use of a diameter instead of a radius, in contrast to calculating the area of ​​a circle.

Sinaumed’s may also have realized that calculating the circumference of a circle is very different from the circumference of a flat figure in general. Even so, if you are already fluent in this topic, you can definitely do problems related to the circumference of a circle as if you were looking for the circumference of another plane.

Circumference Practice Questions

After this, Sinaumed’s will also study a number of problems related to the circumference of a circle, just like after you learned the formula for the area of ​​a circle. When studying mathematics, you will definitely be attached to what is called practice questions.

We hope that Sinaumed’s won’t get bored quickly with the many practice questions that you will find in mathematics. After all, practice questions can help you to master a material in math lessons. In fact, if you rarely work on questions, your understanding of a topic cannot be proven.

In this question practice session, Sinaumed’s will get 3 different types of questions like the previous question practice session. The types of questions will be sorted from the easiest to the most difficult. You can try to work on these questions as much as possible and see the steps if you feel confused.

First Question

The diameter of a circle reaches 20 cm. Based on this information, please determine the circumference of this circle (π = 3.14).
As always, this first problem should be fairly easy for Sinaumed’s to work on. You’ve found all the necessary components into the circumference formula to find the answer to this problem. The calculation will more or less be like this.

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K = π xd
K = 3.14 x 20 cm
K = 62.8 cm

Don’t forget to remind Sinaumed’s to always use the π listed in the questions so he can find the right answer. With this, the answer to the first question is 62.8 cm.

Second Problem

It is known that the circumference of a circle is 77 cm. Based on this information, determine the radius of this circle. (π = 22/7).
In this second problem, Sinaumed’s received an order to find the radius of the circle. At first glance, the second problem regarding the circumference of a circle is similar to the second problem that you have done earlier regarding the area of ​​a circle. For some of you, the second question above might be quite difficult to do.

However, in this second question, Sinaumed’s doesn’t need to worry too much about the difficulty level of this question. Because believe it or not, calculations regarding the circumference of a circle are no more complicated than calculations related to the area of ​​a circle. Try to see the calculation below.

K = π xd
77 cm = 22/7 xd
77 cm ÷ 22/7 = d
24.5 cm = d

Calculations regarding the diameter of the circle for the second problem are already over. However, Sinaumed’s still has to find the radius of this circle, according to the question’s request. So, you have to convert the diameter of the circle into the radius of the circle in the following way.

r = d ÷ 2
r = 24.5 cm ÷ 2
r = 12.25 cm

How about it, Sinaumed’s? Calculations regarding the second problem regarding the circumference of a circle are not as difficult as the second problem regarding the area of ​​a circle, right? And you have managed to find the answer to this problem, where the radius of the circle above is 12.25 cm.
Third Problem

A circle has a circumference of 86.35 cm. Based on this information, what area does this circle have? (π = 3.14)
This third problem will test Sinaumed’s’ understanding not only regarding the circumference of a circle, but also knowledge about the area of ​​a circle. From the questions above, although the information found is about the circumference of a circle, the final question is about the area of ​​a circle.

It could be that the lack of information provided and the thought that Sinaumed’s has to do the third question through a long process will make some of you feel confused before starting to work on it. In fact, believe me, this problem is not as difficult as you think.

Keep in mind that even with the slightest information, Sinaumed’s can still work on this problem if you already understand the formulas and components of the related plane shapes. Let’s try to prove together whether or not this problem is easy to do.

K = π xd
86.35 cm = 3.14 xd
86.35 cm ÷ 3.14 = d
27.5 cm = d
The first step of working on this third problem is complete. And for the rest, Sinaumed’s should be able to continue working on this problem using an understanding of the formula for the area of ​​a circle. This can be started by converting the diameter to the radius first.

r = d ÷ 2
r = 27.5 cm ÷ 2
r = 13.75 cm

After getting the radius of the circle, Sinaumed’s was able to calculate the area of ​​the circle asked in this third problem. You only need to enter all the components that you have got and calculate it slowly, you can definitely find the answer to this problem.

L = π x r²
D = 3.14 x 13.75 cm x 13.75 cm
W = 593.656 cm

Thus, Sinaumed’s’ calculation for the third problem is complete. The answer sought from this problem, namely the area of ​​this circle, is 593,656 cm².

The discussion of this third question is the closing of this article. Hopefully, after reading this article, Sinaumed’s will be able to get the understanding you need about circles, especially regarding the formula for the area of ​​a circle and the formula for the circumference of a circle. To support Sinaumed’s in adding insight, sinaumedia always provides quality and original books so that Sinaumed’s has information #MoreWithReading.

Author: M. Adrianto S.