AMC8 2013

AMC8 2013 · Q18

AMC8 2013 · Q18. It mainly tests Area & perimeter, 3D geometry (surface area).

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?

伊莎贝拉使用一英尺边长的立方体积木建造一个长 12 英尺、宽 10 英尺、高 5 英尺的矩形堡垒。地板和四面墙都是 1 英尺厚。这个堡垒包含多少个积木？

(A) 204 204

(B) 280 280

(D) 340 340

(E) 600 600

Answer

Correct choice: (B)

正确答案：（B）

Solution

There are $10 \cdot 12 = 120$ 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 $9 + 11 + 9 + 11 = 40$ cubes. Hence, the answer is $120 + 4 \cdot 40 = \boxed{\textbf{(B)}\ 280}$.

底面有 $10 \cdot 12 = 120$ 个立方体。然后，对于底面上方的 4 层（因为每个立方体是 1 英尺 × 1 英尺 × 1 英尺，堡垒高 5 英尺，还剩 4 英尺），每层有 $9 + 11 + 9 + 11 = 40$ 个立方体。因此，总数是 $120 + 4 \cdot 40 = \boxed{\textbf{(B)}\ 280}$。

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