Unit Cubes 5 – $n \times n$

Probability Level 1

On an $n \times n \times n$ cube made out of $1 \times 1 \times 1$ unit cubes (with $n \geq 2$ ) with the exterior painted red, how many of the unit cubes will have at least one red face?

n^3 - (n-2)^3

12n^2 + 8

n^3 - n^2 + 12n + 8

8(n-2) + 8

2 solutions

Victor Paes Plinio
May 23, 2014

We have the original cube with ${n}^{3}$ . The center of this cube is not painted, is painted only the exterior. Imagine a hollow cube, the interior part was be removed,the dimension of this part is ${(n-2)}^{3}$ . Therefore the answer is the subtraction between the total cube and the interior cube part or ${n}^{3}-{(n-2)}^{3}$ .

Rogério Carneiro
May 31, 2014

It's just the total number os cubes ( n³) minus the quantity of cubes in the cover layer of the cube (n-2)³.

Unit Cubes 5 – n × n n \times n n × n

2 solutions

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Unit Cubes 5 – $n \times n$