Question

Isabella uses one-foot cubical blocks to build a rectangular fort that is $12$ feet long, $10$ feet wide, and $5$ feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?

$204$

$280$

$320$

$340$

$600$

Video solution:

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Written solution:

The rectangular prism determined by the outside faces has volume $12\cdot10\cdot5=600$ cubic feet. The empty inside is smaller by $2$ feet in length, $2$ feet in width, and $1$ foot in height, so its dimensions are $10\times8\times4$ .

The empty volume is $10\cdot8\cdot4=320$ cubic feet, so the fort contains $600-320=280$ one-foot cubical blocks.

Thus, B is the correct answer.

2013 AMC 8 Problem 18

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Written solution:

Problem 18 in Other Years