Four identical squares are cut from the corners of the rectangular sheet of cardboard shown. This sheet is then folded along the dotted lines and taped to make a box with an open top. The base of the box measures $5 \mathrm{~cm}$ by $4 \mathrm{~cm}$. The volume of the box is $60 \mathrm{~cm}^{3}$. What was the area of the original sheet of cardboard?
(A) $56 \mathrm{~cm}^{2}$
(B) $110 \mathrm{~cm}^{2}$
(C) $156 \mathrm{~cm}^{2}$
(D) $180 \mathrm{~cm}^{2}$
(E) $210 \mathrm{~cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-081.jpg?height=320&width=374&top_left_y=2079&top_left_x=1342)
Since the base of the folded box measures $5 \mathrm{~cm}$ by $4 \mathrm{~cm}$, then the area of the base of the box is $5(4)=20 \mathrm{~cm}^{2}$.

Since the volume of the box is $60 \mathrm{~cm}^{3}$ and the area of the base is $20 \mathrm{~cm}^{2}$, then the height of the box is $\frac{60}{20}=3 \mathrm{~cm}$.

Therefore, each of the four identical squares has side length $3 \mathrm{~cm}$, because the edges of these squares form the vertical edges of the box.

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-139.jpg?height=307&width=371&top_left_y=1733&top_left_x=931)

Therefore, the rectangular sheet measures $3+5+3=11 \mathrm{~cm}$ by $3+4+3=10 \mathrm{~cm}$, and so has area $11(10)=110 \mathrm{~cm}^{2}$.

ANSWER: (B)