Part 1

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In this lesson, we will learn about the circumference of a circle.

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Consider this circle. Now, this circle has the radius, r.

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Now, the formula for the circumference of the circle, C, is given as, 2 pi r.

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Alright, back to this circle.

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The radius of this circle is r. Now, if we draw a line from the center, to here. We will also have the radius r.

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Notice that, this is the diameter of the circle.

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We can find the diameter, by adding r, with r. This gives 2r.

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By letting the diameter be, 'D'. We have, 2 'R' equals to, 'D'.

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Keeping this in mind, notice that, this term has '2', 'R'. By rearranging, we have pi 2 r.

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Since 2'R' is equals to 'D'. This term becomes, pi 'D'.

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Hence, the circumference of the circle is equals to, 2 pi r, or pi D.

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That is all for this lesson. The next video will show some examples on using these formulas.

Part 2

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Let's take a look at some examples, on using the formula for the circumference of a circle.

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In these examples, we take pi as 3.14.

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Find the circumference of this circle, with the radius of 3cm.

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Now, we can start with the formula for the circumference of a circle, 'C' equals to, 2 pi r.

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Since the radius is given as 3cm, we can substitute 'r' with 3..

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Similarly, since pi is given as 3.14, we can substitute this with, 3.14.

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Now, let's calculate this.

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3.14, multiply with 3, gives 9.42.

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2, multiply with 9.42, gives 18.84.

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Hence, we have 'C' equals to, 18.84.


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Now, this number has no meaning unless we include the unit for it.

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Since the radius of the circle is in centimeter, the circumference must also be in centimeter.

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Hence, the circumference of the circle is, 18.84cm.

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Next example. Find the diameter of this circle, when its circumference is 15.7ft.

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Since we are finding the diameter, we can use the formula, 'C' equals to, pi 'D'.

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We can see that, the circumference, and pi are given. Hence, we can find the diameter of the circle, by solving the equation for 'D'.

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Here’s how. The circumference is given as 15.7. Hence, we can substitute 'C' with 15.7.

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Next, since pi is given as 3.14. We can substitute this, with 3.14.

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To find 'D', we need to remove 3.14.

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We can do so, by dividing both sides of the equation with 3.14.

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Hence, we get, 15.7 over 3.14 equals to 'D'.

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15.7, divided by 3.14, gives 5.

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Now, we have 'd', equals to 5.

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Let’s rewrite this equation so that it looks neater.

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Now, let’s include the unit for this number. Since the circumference is given in ft, the diameter will also be in feet.

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Hence, the diameter of the circle is 5 ft.

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That is all. Try out the practice question to test your understanding.