The radius of a larger circle in the figure above is r cm. Determine the area of the non-shaded portion.

Radius of big semicircle $=r$

Area of big semicircle $=\frac{\pi r^2}{2}$

Radius of small semicircles $=r/2$

Area of smaller semicircle $=\frac{1}{2}\times \frac{\pi r^2}{4}$

Area of 2 smaller semicircles $=\frac{\pi r^2}{4}$

Area of non-shaded region = Area of big semicircle $+2\times$ Area of the smaller semicircles

Area of non-shaded region $=\frac{\pi r^2}{2}+\frac{\pi r^2}{4}=\frac{3\pi r^2}{4}$