posted by danielle on .
so i have this table of values demonstrating the size of a cube to the number of small cubes with one face painted. The table starts with an x value (or number of small cubes) at 3x3x3, and goes up to 8x8x8. I need to fill in the y-column (or number of small cubes with one face painted). They have only given me the 5x5x5 corresponding y-value which is 54 as well as the 7x7x7 corresponding y value which is 150. I need to find a formula of some sort to find the rest. i don't know how to do this.. please help me.
Drawing a picture helps.
In a 3x3 side of a cube there is 1 interior square, all the rest are edge pieces. Since there are 6 sides to a cube y for a 3x3 = 6
In a 4x4 there are 4 interior squares.
In a 5x5 there are 9 interior squares.
In a 6x6 there are 16 interior squares.
Notice a pattern yet. The number of interior squares is a perfect square
So the formula is y = 6*((n-2)^2)