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