12. The diagram shows a wooden cube of side $3 \mathrm{~cm}$ with a smaller cube of side $1 \mathrm{~cm}$ cut out at one corner. A second cube of side $3 \mathrm{~cm}$ has a cube of side $1 \mathrm{~cm}$ cut out at each corner.
How many faces does the shape formed from the second cube have?
A 6
B 16
C 24
D 30
E 36
Solution
D

A standard cube has six faces. When a cube is removed from one corner, the number of faces increases by three, as shown in the diagram in the question. Therefore, the cube with a smaller cube cut out at each of its eight corners has a total of $(6+8 \times 3)$ faces. Therefore the second cube has 30 faces.