CSAT 2024

Q. Which is the least possible number of cuts required to cut a cube into 64 identical pieces?

a) 8
b) 9
c) 12
d) 16
Correct answer: b) 9

Question from UPSC Prelims 2024 CSAT

Explanation : 

Least possible number of cuts

Let’s approach this step-by-step:
1) We need to divide the cube into 64 identical pieces. This means we need to divide each dimension of the cube into 4 equal parts (4 x 4 x 4 = 64).
2) For each dimension, we need 3 cuts to divide it into 4 equal parts.
3) So, we need:
– 3 cuts parallel to the xy-plane
– 3 cuts parallel to the yz-plane
– 3 cuts parallel to the xz-plane
4) In total, this gives us 3 + 3 + 3 = 9 cuts.
Therefore, the least possible number of cuts required to cut a cube into 64 identical pieces is 9.
The correct answer is b) 9

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