Area of an annulus

Text

Two concentric circles have radii whose difference is $8$ cm; the smaller radius is $\dfrac35$ of the larger. Compute the area of the annulus between the two circles.

Solution

Let $R$ be the larger radius and $r=\dfrac35 R$ the smaller. From the difference: $R-\frac35R=\frac25R=8\ \Longrightarrow\ R=20\ \text{cm},\quad r=12\ \text{cm}.$ Area of the annulus: $\mathcal A=\pi(R^2-r^2)=\pi(400-144)=256\pi\approx804.25\ \text{cm}^2.$ $\boxed{\mathcal A=256\pi\approx804.25\ \text{cm}^2}$