2009 AMC 8 Problems/Problem 25
Contents
Problem
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is foot from the top face. The second cut is foot below the first cut, and the third cut is foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
Solution 1
The tops of , , , and in the figure formed has sum as do the bottoms. Thus, the total so far is . Now, one of the sides has area one, since it combines all of the heights of , , , and , which is . The other side also satisfies this. Thus the total area now is . From the front, the surface area is half, because if you looked at it straight from the front it would look exactly like , with surface area half. From the back it is the same thing. Thus, the total is , or .
Solution 2
The top parts and the bottom parts sum to 8. The sides add on another 2. Therefore, the only logical answer would be since it is the only answer greater than 10.
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.