Question

What is the formula for finding circumference?

Answer 1

Hint: In this problem we need to calculate or find the circumference. So, we will first look into what is circumference and definition of the circumference. After that we will move to some basic geometric shapes and according to definition, we will calculate the circumference of difference shapes.

Complete step-by-step answer:
In the problem we have the term circumference.
Circumference is nothing but the length that is occupied by the boundary line or outline of any geometric shape. Circumference is also termed as perimeter. As we can see that circumference is length so it is expressed in terms of meters or centimeters.
The basic method that is used to calculate the circumference or perimeter of any shape is that assuming the closed shape is opened such that it forms a straight line and the length of the straight line is considered as circumference or perimeter.
Let us consider a rectangular shape of length $l$ and width $b$ as shown in below figure.

Let us assume that the closed shape $ABCD$ is opened as

Now the circumference or perimeter of the rectangle is the length of the above shown line which is equal to
$\begin{align}
  & P=l+b+l+b \\
 & \Rightarrow P=2\left( l+b \right) \\
\end{align}$
Hence the perimeter or circumference of the rectangle is $2\left( l+b \right)$.
Now consider a circle of radius $r$ as shown in below

For calculating circumference of the circle, the above-mentioned method is not used since it is curve shaped. For this we can take a thread and trace the path of the circle with the thread and mark the end point on thread. Now the length of the thread up to the marked point is considered as the perimeter or circumference of the circle. Anyway, finding the perimeter of the circle from this method is not possible at all times. So, we have the formula for calculating the circumference of circle as
$C=2\pi r$

Note: In this problem we have not discussed how to find circumference or perimeter for rectangle and circle only. We can also follow the method which is used to calculate the circumference of a rectangle, for other geometric shapes.