Question

Find the circumference of the circle with the following radius. (Take $ \pi = \dfrac{{22}}{7} $ )
I. $ 14cm $
II. $ 28cm $
III. $ 21cm $

Answer 1

Hint: As we can see that we have the radius given in the question and we have to find the circumference of the circle. We can put the value of radius in the formula and solve it. The formula of the circumference of the circle is $ C = 2\pi r $ , where $ r $ is the radius of the circle. So we can find the circumference in all the three different cases of radius.

Complete step by step solution:
I.In the first case we have a radius of $ 14cm $ . First of all let us draw the diagram of the given radius with a circle.

In the above figure we have O as the centre of the circle and radius is $ OA $ i.e.
 $ OA = 14cm $ .
Now the formula of the circumference is $ 2\pi r $ and here we have
  $ r = 14cm $ and $ \pi = \dfrac{{22}}{7} $ .
By putting the value in the equation we have
 $ C = 2 \times \dfrac{{22}}{7} \times 14 $ .
On solving it gives us the value
  $ C = 88cm $ .
Hence the circumference of the circle is $ 88cm $ .

II.In the second case, we have a radius of $ 28cm $ .
Let us again draw the diagram of the circle with radius:

In the above figure we have O as the centre of the circle and radius is $ OB $ i.e.
  $ OB = 28cm $ .
We know the formula of the circumference is $ 2\pi r $ and in this figure we have
 $ r = 28cm $ and $ \pi = \dfrac{{22}}{7} $ .
By putting the value in the equation we have
  $ C = 2 \times \dfrac{{22}}{7} \times 28 $ .
On solving it gives us the value;
  $ C = 176cm $ .
Hence the circumference of the circle is $ 176cm $ .

III.Now we will draw the diagram of the circle with radius $ 21cm $

From the above figure we have O as the centre of the circle and radius is $ OP $ i.e.
 $ OP = 21cm $ .
Now the formula of the circumference is $ 2\pi r $ and here we have
  $ r = 21cm $ and $ \pi = \dfrac{{22}}{7} $ .
So by putting the value in the equation we can write
  $ C = 2 \times \dfrac{{22}}{7} \times 21 $ .
On solving it gives us the value
  $ C = 132cm $ .
Hence the circumference of the circle is $ 132cm $ .

Note: We should note that we can also take the value of $ \pi $ as $ 3.14 $ in solving the problem, if no such instruction were given. The circumference of the circle is defined as the linear distance around it or in other words we can say that if a circle is opened to form a straight line then the length of that line will be the circle’s circumference.