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

Given difference $=$ Circumference $-$ radius $=37$

$\Rightarrow 2\pi r-r=37$

$\Rightarrow r\left(2\pi -1\right)=37$

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

$\Rightarrow r\left(\frac{44}{7}-1\right)=37$

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

$\Rightarrow r=37\times \frac{7}{37}$

$\therefore r=7$ cm

Area $=\pi r^2$

$=\frac{22}{7}\times 7\times 7$

$=22\times 7$

$=154{\text{ cm}}^2$