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 ?
I. The minimum number of cuts is 9.
II. The number of smaller pieces which are not painted on any face is 6.
Select the correct answer using the code given below :
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
To divide a cube into 60 equal smaller cubes/pieces with minimum cuts, factor 60 as 3×4×5, requiring (3−1)+(4−1)+(5−1) = 2+3+4 = 9 cuts along the three axes. So statement I is correct. The unpainted inner pieces form a cuboid of dimensions (3−2)×(4−2)×(5−2) = 1×2×3 = 6 pieces, confirming statement II. Hence both statements are correct.
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