Solution:

Area of ring = A(larger circle) - A(smaller circle)

$\therefore Area of ring = \pi r1^{2} - \pi r2^{2} = \pi ( r1^{2} -r2^{2})$

$\therefore 2 \pi r1 = 75$

$\therefore r1 = \frac{75}{2\pi}$

$\therefore 2 \pi r2 = 55$

$\therefore r2 = \frac{55}{2 \pi}$

$Area of ring = \pi(r1^{2} - r2^{2})$

$=\pi\left(\left(\frac{75}{2 \pi}\right)^{2}-\left(\frac{55}{2 \pi}\right)^{2}\right)$

$=206.9$