How to find the circumference of a circle?

How to find the circumference of a circle?

Now that we have looked at the area of ​​a triangle, the next thing we need to look at is the perimeter of the triangle. Yes it is.

You can easily find the perimeter of a triangle. You will tell it simply. Knowing the measurements of three sides is enough. It is necessary to add all three. It is a simple additional sum.

However, you say that we will look into it properly. Well let's see.

An equilateral triangle means that all three sides are equal. So multiplying one of its sides by three is sufficient. For example, the perimeter of an equilateral triangle is 3a units if its side measurement is denoted by the variable a.

If an isosceles triangle is denoted by variables a and b with respective to equal and unequal side, its perimeter is 2a + b units.

An scalene triangle means that all three side measures are unequal and if its side measures are denoted by variables a, b, c then its perimeter will be a + b + c units.

Now we know well about perimeter and area of ​​three types of shapes namely square, rectangle and triangle. Also, we know the area of ​​the parallelogram as well. What's next? Is it a circle?

Let's start from the circumference of the circle. How to find the formula for the circumference of a circle?

You are well aware of the circle. It will be like Mary Biscuit. It will be like the dosa that mom bakes. Bangles are worn on the hands of sisters.

Can't we draw the circle by fitting the pencil to the compass? When you draw like that, you know very well that the center of the circle is the point where the point of compass falls, and the radius is the distance from that center to the circle we draw.

Now if we draw a circle using the compass, then the circle is called the arc of the circle. i.e. the circumference of the circle.

The center of the circle is the point at which a line drawn through it joining the two sides of the circle is the diameter. That is, two radii on either side from the center of the circle. That's the main point that we observe.

That means if you put one diameter it is equivalent to drawing two radii. So we can say that diameter = 2 × radius?

Why are you saying this you ask? Therein lies some mathematical point. Shouldn't we find the formula for the circumference of a circle?

Square, rectangle, triangle, etc. can be accurately measured for sides. We can calculate the circumference by adding the measurements. They give the side measurements when they ask for the calculation. We can add up and say the perimeter.

What to do in a circle? There is no side to it. How to measure? What to keep a side? How to find perimeter without giving side measures?

The only size we know for a circle is its radius. We can calculate the diameter by multiplying that radius twice. That's all we know. Given this, how do we find the perimeter?

We are now going to cover a method for this.

Do you know what you are going to do now?

Draw as many circles as you like with a compass and a pencil.

Multiply the radius of each circle drawn by two. Also you draw the circumference of the circles with a thread and fix it to its circumference and keep it on the scale and see how much it measures.

Don't ask me if I have to hold the string or thread like this to find the circumference of the circle. Wait a minute. Let's create a formula for that. After that we don't need thread, nothing.

Now what you need to do is measure twice the radius of each of the circles you have drawn and list the circumference as follows. List and calculate the ratio of the circumference to twice the radius and add to the list. Or you can fill out the table by measuring different sizes of bangles. Do whatever is convenient for you.

Circle	Twice the radius	Circumference of the circle that measure by string	Circumference / twice the radius
First circle
Second circle
Third circle
Fourth circle
Fifth circle

 

As many circles as you have drawn, tabulate and list them like this and find the ratio we asked you to find.

Now the ratio of the circumference to twice the radius that you found is approximately close to 3.14?

That's how it will be.

Using this ratio we are now going to derive the formula for the circumference of a circle. that is,

Circumference of the circle / Twice the radius = 3.14

Now for the equation of twice the radius as the denominator of this side of the equation Multiply to the right. ie as cross multiplication.

So circumference of circle = 3.14 × twice radius

The radius of a circle is denoted by r, the first letter of the English word Radius. Thus if radius is taken as variable r

Isn't the circumference of the circle = 3.14 × 2r?

The value 3.14 is represented by 22/7 and π. Thus we can now denote the circumference of the circle as π × 2r. It can be expressed as 2πr units for convenience of multiplication and formula. This is the formula for the circumference of a circle. That is, if we know the radius of a circle, we can find its circumference. No need to carry the thread and wander. Have we found the formula for the circumference of a circle?

What's next you ask? Let's move on to the formula for the area of ​​a circle. Think about it and find out. Let's see tomorrow.

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