A cube with an edge length of 4 inches is

painted on all of its sides. The large cube is then cut into 64 cubes, each with an edge length of 1 inch. If you spread the pieces out, what percent of the total surface area of all

the cubes is now painted?

The surface area of a cube is calculated through the equation,

SA = 6s²

For the first cube, with an edge length of 4 inches, the surface area is,

SA = 6 (4 in) ² = 96 in²

This is the total area covered by paint. Then, cutting large cube into 64 cubes with 1-inch edge length will give us a total surface area of,

SA₂ = 64 x 6 x (1 in) ² = 384 in²

To answer the question above, we simply divide SA by SA₂ and multiply the quotient by 100%

((96 in²) / (384 in²)) x 100% = 25%

Therefore, only 25% of the total surface area is now painted.