In the diagram, each partially shaded circle has a radius of $1 \mathrm{~cm}$ and has a right angle marked at its centre. $\mathrm{In}^{2} \mathrm{~cm}^{2}$, what is the total shaded area?
(A) $4 \pi^{2}$
(B) $9 \pi^{2}$
(C) $4 \pi$
(D) $9 \pi$
(E) $3 \pi$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-027.jpg?height=284&width=374&top_left_y=259&top_left_x=1296)
Since the complete angle at the centre of each circle is $360^{\circ}$ and the unshaded sector of each circle has central angle $90^{\circ}$, then the unshaded sector of each circle represents $\frac{90^{\circ}}{360^{\circ}}=\frac{1}{4}$ of its area.

In other words, each of the circles is $\frac{3}{4}$ shaded.

There are 12 circles in the diagram.

Since the radius of each circle is 1 , then the area of each circle is $\pi \times 1^{2}$ or $\pi$.

Therefore, the total shaded area is $\frac{3}{4} \times 12 \times \pi$ or $9 \pi$.

ANSWER: (D)