The difference between the circumference and radius of a circle is 7 cm. Find the area of the circle.

Hint:We will use the formula of the circumference of the circle, that is, $2\pi r$, where r is the radius of the circle. The first relation can be represented as $2\pi r-r=7$. We will find r from here and then use the formula of the area of the circle, that is, $\pi {{r}^{2}}$ in order to find the area of the circle.

Complete step-by-step answer:
It is given in the question that the difference between the circumference and the radius of a circle is 7 cm and we have been asked to find the area of the circle. We know that the circumference of a circle is given by the formula, $2\pi r$, where r is the radius of the circle. Now, it is given in the question that the difference between the circumference and the radius of a circle is 7 cm. So, we get,
Circumference – radius = 7 cm
$\begin{align}
  & 2\pi r-r=7 \\
 & 6.28r-r=7 \\
 & 5.28r=7 \\
 & r=\dfrac{7}{5.28}=1.32cm \\
\end{align}$
Hence, we get the value of the radius of the circle as 1.32 cm. Now, we also know that the area of a circle is given by the formula, $\pi {{r}^{2}}$. So, on substituting the value of r in the formula of the area of the circle, we will get as follows.
Area of the circle = $\pi {{r}^{2}}$
$\begin{align}
  & =3.14\times {{\left( 1.32 \right)}^{2}} \\
 & =3.14\times 1.32\times 1.32 \\
 & =5.47c{{m}^{2}} \\
\end{align}$
Therefore, the area of the circle is $5.47c{{m}^{2}}$.

Note: The possible mistake that the students can make in this question is that they might interchange the formulas of circumference and area of the circle, as they are not clear about the difference between the circumference and area of the circle. So, the students must remember that the formula of circumference of a circle is $2\pi r$ and the formula of the area of a circle is $\pi {{r}^{2}}$.