Question

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?

Answer 1

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.