Problem:
Each corner cube is removed from this cube. The surface area of the remaining figure is
Answer Choices:
A. sq. cm
B. sq. cm
C. sq. cm
D. sq. cm
E. sq. cm
Solution:
In terms of the original cube, three square centimeters are lost from each corner, but three new squares are added as the sides of the cavity in that corner. The total area remains at square centimenters.
Each face had an area of square centimeters originally, so the total area was . Four squares are lost from each face, leaving . But the cavity in each of the eight corners has an area of , so must be added. Finally, .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions