Question:
The difference between the circumference and radius of a circle is $37 \mathrm{~cm}$. Using $\pi=\frac{22}{7}$, find the circumference of the circle.
Solution:
Let the radius of the circle be r and circumference C.
Now,
$C-r=37$
$\Rightarrow 2 \pi r-r=37$
$\Rightarrow r\left(2 \times \frac{22}{7}-1\right)=37$
$\Rightarrow r=\frac{37 \times 7}{37}=7 \mathrm{~cm}$
Now, $C=2 \pi r=2 \times \frac{22}{7} \times 7=44 \mathrm{~cm}$
Hence, the circumference of the circle is 44 cm.