10. The centres of the seven circles shown all lie on the same line. The four smaller circles have radius $1 \mathrm{~cm}$. The circles touch, as shown.
What is the total area of the shaded regions?
A $\pi \mathrm{cm}^{2}$
B $2 \pi \mathrm{cm}^{2}$
C $3 \pi \mathrm{cm}^{2}$
D $4 \pi \mathrm{cm}^{2}$
E $5 \pi \mathrm{cm}^{2}$
SolUtion
B

If the shaded pieces on the right-hand side are reflected in a central vertical line, the total shaded area is then the area of one large circle minus the areas of two small circles. The radius of each large circle is $2 \mathrm{~cm}$ so the shaded area, in $\mathrm{cm}^{2}$, equals $\pi \times 2^{2}-2 \times \pi \times 1^{2}=4 \pi-2 \pi=2 \pi$.