Painted cube cut into 60 pieces
Question
A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct?
- 1.
The minimum number of cuts is 9.
- 2.
The number of smaller pieces which are not painted on any face is 6.
Options
I only
II only
Both I and II
Neither I nor II
Explanation
To minimize cuts for N identical pieces, express N as the product of three factors x y z that are as close to each other as possible. For 60, the optimal factors are 3 4 5. The number of cuts required is (x-1) + (y-1) + (z-1) = 2 + 3 + 4 = 9. Statement I is correct.
The formula for interior, unpainted smaller cubes is (x-2)(y-2)(z-2). Plugging in our dimensions: (3-2)(4-2)(5-2) = 1 2 3 = 6. Statement II is also correct.
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q5
Section
Logical & Analytical Reasoning
Sub-topic
Cube & Painted Faces
Type
Cube & geometry
Difficulty
Hard
Source hint
Spatial reasoning
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