CSAT 2023

Q. 125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side?

(a) 27
(b) 25
(c) 21
(d) 18
Correct Answer: (a) 27

Question from UPSC Prelims 2023 CSAT

Explanation : 

125 identical cubes

In a cubical block, the cubes that are surrounded by other cubes from each side are the internal cubes.

The total number of cubes is 125, which means the cubical block is 5 cubes long, 5 cubes wide, and 5 cubes high (since 5*5*5 = 125).

The internal cubes are those that are not on any of the faces of the large cube. Since each face of the large cube is 5 cubes by 5 cubes, the internal cubes form a smaller cube that is 3 cubes by 3 cubes by 3 cubes (since we subtract the top and bottom layer from the height, and one layer from each side of the width and length).

So, the number of internal cubes is 3*3*3 = 27. Therefore, 27 cubes are surrounded by other cubes from each side..

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