A cube with edge of length 4 is divided into 8 identical cubes. How much greater is the combined surface area of the 8 smaller cubes than the surface area of the original cube?
The surface area of the original cube is .
When the cube is cut into 8 smaller cubes (accomplished by cutting it in half along each axis, see above) then each cube has an edge length of 2, so each has a surface area of . Because there are 8 of them, the total surface area is .
The question asked “how much greater,” so we subtract: . This makes sense in an abstract way, if you think about it. By cutting a cube in half along each axis, you’re doubling the surface area.