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1998 CEMC Gauss (Grade 7) Problems/Problem 23

Problem

A cube measures 10 by 10 by 10 cm. Three cuts are made parallel to the faces of the cube as shown (in three perpendicular directions) creating eight separate solids which are then separated. What is the increase in the total surface area?

$\text{(A)}\ 300 \text{cm}^2 \qquad \text{(B)}\ 800 \text{cm}^2 \qquad \text{(C)}\ 1200 \text{cm}^2 \qquad \text{(D)}\ 600 \text{cm}^2 \qquad \text{(E)}\ 0 \text{cm}^2$

Solution

The original surface area was $6(10^2) = 600$ square centimeters. The surface area of the separate solids are $8(6 \cdot 5^2) = 1200$ cubic centimeters. This is an increase of $\boxed{\text{(D)} \quad 600}$ square centimeters.

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