2000 AMC 8 Problems/Problem 22
Problem
A cube has edge length . Suppose that we glue a cube of edge length on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to
Solution
The original cube has faces, each with an area of square units. Thus the original figure had a total surface area of square units.
The new figure has the original surface, with new faces that each have an area of square unit, for a total surface area of of additional square units added to it. But square unit of the top of the bigger cube, and square unit on the bottom of smaller cube, is not on the surface, and does not count towards the surface area.
The total surface area is therefore square units.
The percent increase in surface area is , giving the closest answer as .
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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