Question

The circumference of a circle is 3.14m Its area will be equal to
A \[4\pi {m^2}\]
B \[\dfrac{\pi }{4}{m^2}\]
C \[4\pi c{m^2}\]
D \[\dfrac{\pi }{4}c{m^2}\]

Answer 1

Hint: In this problem, first we need to find the radius of the circle using the circumference formula. Next, find the area of the circle. Circumference of the circle is a product of the radius and \[2\pi\].

Complete step-by-step answer:
The formula for the circumference of a circle is shown below.
\[P = 2\pi r\]
Here, P is circumference and \[r\] is the radius of the circle.
Substitute 3.14 for P in the above formula to obtain the value of radius \[r\].
\[\begin{gathered}
  \,\,\,\,\,\,3.14 = 2\pi r \\
   \Rightarrow 3.14 = 2\left( {3.14} \right)r \\
   \Rightarrow 2r = 1 \\
   \Rightarrow r = \dfrac{1}{2}m \\
\end{gathered}\]
The formula for the area of the circle is shown below.
\[A = \pi {r^2}\]
Substitute \[\dfrac{1}{2}\] for \[r\] in the above formula, to obtain the area of the circle.
\[\begin{gathered}
  \,\,\,\,\,\,A = \pi {\left( {\dfrac{1}{2}} \right)^2} \\
   \Rightarrow A = \pi \left( {\dfrac{1}{4}} \right) \\
   \Rightarrow A = \dfrac{\pi }{4}{m^2} \\
\end{gathered}\]
Thus, the area of the circle is \[\dfrac{\pi }{4}{m^2}\], hence, option (B) is the correct answer.

Note: The circumference of the circle is also termed as the perimeter of the circle. The circumference of the circle is also calculated as the product of \[\pi \] and diameter of the circle.