Elijah has seven identical wooden unit cubes. He glues them together face-to-face to form a single three-dimensional shape (the figure below illustrates how two cubes are glued together). What is the smallest possible surface area of this new shape ?
A. 24
B. 26
C. 28
D. 30
E. 32

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Worked solution

1. 2026 AMC 8 官方解析

方法一：粘1次，表面积少2个面，
想要表面积尽量小，粘的次数尽量多，至多9次，
$S_{\text{表}} = 7 \times 6 \times 1^2 - 9 \times 2 = 24$ .

方法二： $S_{\text{总}} = 6 \times 1 \times 1 \times 7 = 42$
$S_{\text{min}} = 42 - 2 \times 9 = 24$

Answer

A. 24

AI analysis — may contain mistakes.

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