2022 Fermat Problem 17

An aluminum can in the shape of a cylinder is closed at both ends. Its surface area is 300 cm^2. If the radius of the can were doubled, its surface area would be 900 cm^2. If instead the height of the can were doubled, what would its surface area be?

(The surface area of a cylinder with radius r and height h is equal to 2\pi r^2 + 2\pi rh.)

\textbf{(A)}\ 450 \text{ cm}^2\quad \textbf{(B)}\ 600 \text{ cm}^2\quad \textbf{(C)}\ 750 \text{ cm}^2\quad \textbf{(D)}\ 375 \text{ cm}^2\quad \textbf{(E)}\ 300 \text{ cm}^2

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.