Cut a small cube with edge length 2 cm inside of a 10 cm × 8 cm × 5 cmbox. What is the surface area of the remaining object?

cm^{2}

We
see that we are removing at 2 by 2 area from the original surface area, but we
are adding 5 more of these 2 by 2 square faces to the surface area. Thus, the
increased surface area is 4, 2 by 2 faces of the small box. The surface area of
the original box is (10 × 8 + 10 × 5 + 8 × 5) × 2 = 340 cm^{2}. Now we
add 2 × 2 × 4 = 16 to 340 to get a total surface area of 356 cm^{2}.