Question

Design an expression that can be used to find the surface area of tower n cubes tall

Answer 1

Answer: The surface is (4*n + 2)*L^2

Explanation:

The surface of a cube is equal to 6 times the area of one of the sides.

So if the sides of the cube have a length L, we have that the area of one face is L^2, and the surface of the cube is 6*L^2

Now, if we put n of those cubes in a tower, we will have a shape were the bottom and the top still have an area of L^2, then the total area of the bottom and the top is 2*L^2

But each one of the sides has two sides of length L, and two sides of length n*L (n times the length of one of the sides), then the area of each side is equal to n*L*L = n*L^2

and we have 4 sides, then the total area of the sides is 4*n*L^2

Then the total surface of the tower is:

A = 4*n*L^2 + 2*L^2 = (4*n + 2)*L^2