A cube of side 125 cm is painted red on all the faces and then cut into smaller cubes of sides 25 cm each. Find the number of smaller cubes having at least two faces painted.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 44.
The number of smaller cubes having at least two faces painted = Total number of cubes -(Number of cubes with one no face painted + Number of faces with one face painted) = 125 - ((a - 2)3 + 6(a - 2)2)
where a = Length of the bigger cube ÷ Length of smaller cube = 125 ÷ 25 = 5
= 125 - ((5 - 2)3 + 6(5 - 2)2)
= 125 - ((3)3 + 6(3)2)
= 125 - (27 + 6(9))
= 125 - (27 + 54)
= 125 - 81
= 44