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What is the method to measure the length of an arc of a circle

Here is the detail about What is the method to measure the length of an arc of a circle. You will find different methods for the measurement of the length of only a single arc of a circle. There are different methods for it but the most preferred method which is easily understandable by the students is described below.

Method to measure the length of an arc of a circle:

There are 2 methods through which you can easily find out the length of an arc of a circle.

What is the method to measure the length of an arc of a circle

Method 1:

It is a very easy method and you can easily understand the steps of this method. So you have to follow some steps to find out the length of an arc of a circle. So basically the formula through which you will be able to calculate the length of an arc of a circle is 2πr(θ/360).  In this formula π has a value that is equal to 3.14, while r is the radius of the circle, θ equals the measurement of the arc’s central angle in degrees. As it seems to be difficult we will give you some steps which you have to follow.

  • Step 1:

So in the very first step, you have to put the the length of radius of a circle into the formula so you can conclude the required answer which is the arc length of the circle. So we will give you an example so that you can understand it easeasilywhich is equal to 10cm so the main formula will be :

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2*10π(θ/360).

  • Step 2:

Now you have to put the value of the angle which is in the main formula.  But you have to remember one thing the value must be in degrees. If the value in a question is in radians your first step will be to convert the radians into degrees and then put it in the main formula. For example, if θ is equal to 135° then the formula that you have set in step 2 will be

2*10π(135°/360).

  • Step 3:

Now the next step is to multiply the value of the radius which is 10cm with 2π. So, the value of π is equal to 3.14. Now you have to multiply 3.14 by 2 and then by 10cm which is the value of the radius of the circle. So now the formula will look like

Arc length =2(3.14)(10)(135/360)

The value which comes after the multiplication of 10cm with 2π is 62.8. So formula will be written as

Arc length=(62.8)(135/360)

  • Step 4:

Now you have to divide θ which is the arc’s central angle with 360.

For example,

 After dividing the arc’s central angle which must be in degrees with 360 degrees you will get the value that is 0.375. So the formula will be

Arc length =(62.8)(135/360)

Arc length=(62.8)(0.375)

  • Step 5:

Now multiply the two numbers together.

For example, after multiplying 62.8 by 0.375 the resulting value will be 23.55

Arc length = (62.8)(0.375)

Arc length=23.55

This 23.55 is the arc length of the circle which you can get after performing 5 steps. So you can conclude this required value by using radius oa f the circle whose value was 10 cm,θ which is in degrees its value was 135 degrees.

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Method 2:

There is also one more method through which you can find out the arc length of a circle. This is also a very easy method. You can opt for any of the methods that you find easily according to your knowledge. This method also contains various steps that you have to follow if you want to find out the arc length of a circle.

  • Step 1:

So in the very first step, you have to consider the formula of arc length as a product of θ and r.

So arc length = θr

Here θ is the central angle of the arc which is in radians. As in the previous method, θ was in degrees but in this method, you have to consider θ in radians. While r is the radius of the circle in the above formula. After multiplying θ and radius you will find out the arc length of the circle.

  • Step 2:

So now in the second step, you have to put the value of r which is the radius of the circle, and then multiply it with θ which is the central angle of the arc.

For example, if you will assume the value of the radius of the circle as 10 cm then the formula will look like this;

Arc length = θ(10)

  • Step 3:

So in step 3, you will put the value of the central angle of the arc that is θ. If you find out that the central angle is in degrees then you have to convert it into radians if you want a final answer that you require.

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For example, if θ is equal to 2.66 then you will multiply it with 10 ..

So arc length = 2.36(10)

  • Step 4:

Now in the last step, you have to multiply θ which is 2.36 with a radius which is 10 cm.

So arc length = 2.36(10)

Arc length= 23.6cm

This is the required value which you will find out after completing all the steps. This is the arc length of the circle which you will calculate by the product of the central angle of the arc with the radius of the circle. This is a very easy method so can follow any of the methods that we provide you in the Thai article to find out the arc length of the circle.

Conclusion:

To find out the arc length of the circle there are 2 methods. You can opt for any of the methods to find out the required answer. In this article, you will find out every step of both methods.

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