UKMT Pink Kangaroo, 2023

A square of side-length $30\text{ cm}$ is divided into nine smaller identical squares. The large square contains three circles with radii $5\text{ cm}$ (bottom right), $4\text{ cm}$ (top left) and $3\text{ cm}$ (top right), as shown. What is the total area of the shaded part?

(A) $400\text{ cm}^2$ (B) $500\text{ cm}^2$ (C) $(400+50\pi)\text{ cm}^2$ (D) $(500-25\pi)\text{ cm}^2$ (E) $(500+25\pi)\text{ cm}^2$