Question

What is the area of the circle with the circumference of \[6.28\]?

Answer 1

Hint: To find the area of the circle when circumference is given, firstly we have to find out the radius with the help of circumference given and then apply it in the formula of area of the circle. The formula of area of circle is \[a=\pi {{r}^{2}}\] and the formula of circumference of circle is \[c=2\pi r\]. Circumference is nothing but the perimeter of the circle.

Complete step-by-step solution:
Now let us find out the area of the circle with circumference is 6.28.
Firstly let us find out the radius of the circle. We can find it out from the circumference.
Let us consider \[\pi =3.14\]. Now, we will write the formula for circumference and substitute the values as below,
\[\begin{align}
  & \Rightarrow c=2\pi r \\
 & 6.28=2\times 3.14\times r \\
 & \dfrac{6.28}{2\times 3.14}=r \\
\end{align}\]
On cancelling the terms, we get
\[r=1\]
\[\therefore \] We get the radius of the circle as \[r=1\].
Now we will substitute this value into the formula of area of circle i.e. \[a=\pi {{r}^{2}}\] and we will get
\[\begin{align}
  & a=\pi {{r}^{2}} \\
 &\Rightarrow a=3.14\times 1\times 1 \\
 &\Rightarrow a=3.14 \\
\end{align}\]
\[\therefore \] The area of the circle with circumference \[6.28\] is \[a=3.14\].

Note: This question can also be solved by the formula \[a=\dfrac{{{c}^{2}}}{4\pi }\]. By directly substituting the value of circumference we can find out the area. Before finding out the required values, be sure of the formulas to be used. The circle with radius =1, circumference = 6.28 and area=3.14 is plotted below.