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Difference between revisions of "1998 CEMC Gauss (Grade 7) Problems/Problem 23"

(Created page with "== 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 sol...")
 
(No difference)

Latest revision as of 15:55, 29 January 2021

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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