Question 2.43: Determine the area of the annulus shown in Figure 2.23, whic...

The shaded area (similar to a doughnut in shape) is the area of the annulus we require. We know both the inner and outer radii, so we can treat this shape as the difference between the outer and inner circles. We know that the area of a circle = πr². Now our two circles have two different radii, with R = 8 cm and r = 5 cm. Since the area of the annulus A is the difference between these two circles, we may write:

A = πR² − πr²      or      A = π (R² − r²).

Then, substituting the appropriate values of the radii:

\begin{aligned} A=\pi\left(8^2-5^2\right)=\pi(64-25) &=(39)\left(\frac{22}{7}\right) \\ &=122.6 \ cm ^2 \end{aligned}.