14. A square of side-length $30 \mathrm{~cm}$ is divided into nine smaller identical squares. The large square contains three circles with radii $5 \mathrm{~cm}$ (bottom right), $4 \mathrm{~cm}$ (top left) and $3 \mathrm{~cm}$ (top right), as shown. What is the total area of the shaded part?
A $400 \mathrm{~cm}^{2}$
B $500 \mathrm{~cm}^{2}$
C $(400+50 \pi) \mathrm{cm}^{2}$
D $(500-25 \pi) \mathrm{cm}^{2}$
$\mathrm{E}(500+25 \pi) \mathrm{cm}^{2}$
Solution
B

The sum of the areas of the two smaller grey circles is the same as that of the white circle since $(3 \pi)^{2}+(4 \pi)^{2}=(5 \pi)^{2}$. This means that the shaded area is the same as the area of the five of the smaller squares. Each of the smaller squares has and area of $10 \mathrm{~cm} \times 10 \mathrm{~cm}=100 \mathrm{~m}^{2}$. The shaded area is then $5 \times 100 \mathrm{~cm}^{2}=500 \mathrm{~cm}^{2}$.