If the difference between the circumference and radius of a circle is 37 cm,

We know that circumference; $\mathrm{C}$ of the circle with radius $r$ is equal to $2 \pi r$.

We have given difference between circumference and radius of the circle that is $37 \mathrm{~cm}$.

$\therefore C-r=2 \pi r-r$

$\therefore(2 \pi-1) r=37$

Substituting $\pi=\frac{22}{7}$ we get,

$\therefore\left(2 \times \frac{22}{7}-1\right) r=37$

$\therefore\left(\frac{44-7}{7}\right) r=37$

$\therefore\left(\frac{37}{7}\right) r=37$

Dividing both sides of the equation by $\frac{7}{37}$, we get, $\therefore r=7$

Therefore, circumference of the circle will be 

$2 \pi \mathrm{r}=2 \times \frac{22}{7} \times 7$

$=44 \mathrm{~cm}^{2}$

Hence, the correct choice is (b).