Question

The difference between the circumference and the radius of a circle is 37 cm. Find the area of the circle.

Answer 1

Let the radius of the circle be r cm.
According to the question, we have:

$2\mathrm{\pi }r-r=37$
$$\begin{gathered} \Rightarrow r\left(2\mathrm{\pi }-1\right)=37 \\ \Rightarrow r=\frac{37}{2\times {\displaystyle \frac{22}{7}}-1}=\frac{37\times 7}{37}=7\mathrm{cm} \end{gathered}$$

Now,
Area of the circle = $\mathrm{\pi }{r}^2$
$$\begin{gathered} =\frac{22}{7}\times 7\times 7 \\ =154{\mathrm{cm}}^2 \end{gathered}$$