Solution:

Area of the region in between outer and inner circle = Area of outer circle – Area of inner circle

Area of the outer circle $= \pi {\left(18\right)}^2 = 324 \pi c{m}^2$

Area of the inner circle $= \pi {\left(7\right)}^2 = 49 \pi c{m}^2$

So, area of the required region$= 324 \pi – 49\pi = 275 \pi c{m}^2$