2013 AMC 8 Problems/Problem 18
Contents
Problem
Isabella uses one-foot cubical blocks to build a rectangular fort that is feet long, feet wide, and feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?
Solution 1
There are cubes on the base of the box. Then, for each of the 4 layers above the bottom (as since each cube is 1 foot by 1 foot by 1 foot and the box is 5 feet tall, there are 4 feet left), there are cubes. Hence, the answer is .
Solution 2 (Complementary Counting)
We can just calculate the volume of the prism that was cut out of the original box. Each interior side of the fort will be feet shorter than each side of the outside. Since the floor is foot, the height will be feet. So the volume of the interior box is .
The volume of the original box is . Therefore, the number of blocks contained in the fort is .
Video Solution by OmegaLearn
https://youtu.be/FDgcLW4frg8?t=5261
~ pi_is_3.14
Video Solution 2
https://youtu.be/WlMUXUloTFM Soo, DRMS, NM
Video Solution 3
https://youtu.be/zFNf8WxBdoY ~savannahsolver
See Also
(Other problems)
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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