下面的几何体由 1 厘米的正方体组成。最少需要往该几何体中添加多少个正方体,才能使其成为一个正方体? 答案:___

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完整解法

18

1. Determine the dimensions of the smallest possible cube that can enclose the solid.

The maximum height of the solid is 44 cubes.
The width consists of a left column, a middle column, and a right column, making it 33 cubes wide.
The depth consists of the back column and a row of 33 cubes extending forward, making it 1+3=41 + 3 = 4 cubes deep.
To form a cube, all dimensions must be equal to the largest dimension, which is 44. Thus, the target cube must be 4×4×44 \times 4 \times 4.

2. Calculate the total number of cubes required for the $4 \times 4 \times 4$ cube.

Total cubes needed =4×4×4=64= 4 \times 4 \times 4 = 64

3. Count the number of cubes currently in the solid.

Number of cubes =4 (tallest column)+3 (left column)+2 (right column)+3 (forward row)+1 (in front of tallest)+1 (between columns)=14= 4 \text{ (tallest column)} + 3 \text{ (left column)} + 2 \text{ (right column)} + 3 \text{ (forward row)} + 1 \text{ (in front of tallest)} + 1 \text{ (between columns)} = 14

4. Calculate the number of cubes to be added.

Cubes to add =64−14=50= 64 - 14 = 50

答案

5050

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