AMC8 1998
AMC8 1998 · Q21
AMC8 1998 · Q21. It mainly tests 3D geometry (volume).
A $4 \times 4 \times 4$ cubical box contains 64 identical small cubes that exactly fill the box. How many of these small cubes touch a side or the bottom of the box?
一个 $4 \times 4 \times 4$ 的立方体盒子装有 64 个完全填满盒子的小立方体。其中有多少个小立方体触及盒子的侧面或底部？
(A)
48
48
(B)
52
52
(C)
60
60
(D)
64
64
(E)
80
80
Answer
Correct choice: (B)
正确答案：（B）
Solution
Answer (B): The $2 \times 2 \times 3$ core contains all of the small cubes that do not touch a side or the bottom. These 12 cubes are subtracted from 64 to leave 52.
答案（B）：$2 \times 2 \times 3$ 的核心包含所有不接触侧面或底面的 小立方体。这 12 个立方体从 64 中减去，剩下 52。
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