Question : Directions: A cube is painted on all surfaces with an orange colour and is divided into 27 equal cubes. How many cubes will have only one face painted?
Option 1: 6
Option 2: 4
Option 3: 9
Option 4: 5
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Correct Answer: 6
Solution : When a cube is divided into N equal parts, the number of cuts can be calculated as the cubic root of the given number N.
So, cube root of 27 = 3
N = 27; n = 3
The formula used for the number of cubes for 1 side painted surface = 6 × (n – 2)
2
= 6 × (3 – 2)
2
= 6 × (1)
2
= 6 × 1 = 6
So, 6 cubes are painted on one side. Hence, the first option is correct.
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