A cube of sides 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each. Find the number of smaller cubes having only one face painted.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 150.
Here cube of n x n formulae is:
* Cube of no side painted = (n - 2)³
* Cube of one side painted = 6 × (n - 2)²
* Cube of two side painted = 12 * (n - 2)
* Cube of three sides painted = Always 8
A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides of 7 cm each.
= n = 7
Number of smaller cubes having only one face painted = 6 × (n - 2)²
= Number of smaller cubes having only one face painted = 6 × (7 - 2)²
= Number of smaller cubes having only one face painted = 6 × 5²
= Number of smaller cubes having only one face painted = 6 × 25
→ Number of smaller cubes having only one face painted = 150
Hence, the correct answer is '150'.