A cube measures $10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}$. Three cuts are made parallel to the faces of the cube as shown creating eight separate solids which are then separated. What is the increase in the total surface area?
(A) $300 \mathrm{~cm}^{2}$
(B) $800 \mathrm{~cm}^{2}$
(C) $1200 \mathrm{~cm}^{2}$
(D) $600 \mathrm{~cm}^{2}$
(E) $0 \mathrm{~cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-105.jpg?height=282&width=290&top_left_y=680&top_left_x=1443)
A cube measures $10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}$. Three cuts are made parallel to the faces of the cube as shown creating eight separate solids which are then separated. What is the increase in the total surface area?
(A) $300 \mathrm{~cm}^{2}$
(B) $800 \mathrm{~cm}^{2}$
(C) $1200 \mathrm{~cm}^{2}$
(D) $600 \mathrm{~cm}^{2}$
(E) $0 \mathrm{~cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-473.jpg?height=369&width=374&top_left_y=1282&top_left_x=1344)

## Solution

One cut increases the surface area by the equivalent of two $10 \mathrm{~cm} \times 10 \mathrm{~cm}$ squares or $200 \mathrm{~cm}^{2}$.

Then the three cuts produce an increase in area of $3 \times 200 \mathrm{~cm}^{2}$ or $600 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-473.jpg?height=420&width=357&top_left_y=1739&top_left_x=1361)

ANSWER: (D)