UPSC Prelims 2023·CSAT·Quantitative Aptitude·Geometry and Mensuration

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

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Last updated 23 May 2026, 3:31 pm IST
  1. A27Correct
  2. B25
  3. C21
  4. D18

Explanation

To solve this, we first find the dimensions of the large cubical block. Since there are 125 identical cubes, and the cube root of 125 is 5, the block is a 5 by 5 by 5 arrangement. Cubes that are surrounded by other cubes from each side are the inner cubes that do not touch any of the outer faces. To find the number of these inner cubes, we subtract the two outer layers from each dimension. Subtracting 2 from each side of the 5 by 5 by 5 block gives us an inner core of 3 by 3 by 3 cubes. Calculation: 3 multiplied by 3 multiplied by 3 equals 27. Therefore, 27 cubes are completely surrounded by other cubes. The correct answer is A.
Quantitative Aptitude: 125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each
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