This little stack is made of 1 cm cubes glued together. It is dipped in paint, base and all. What is the total painted area?

Four cubes have $4\times 6=24$ faces, but each place where two cubes are glued hides two faces. There are 3 glued joins, hiding 6 faces: $24-6=18$ squares of $1{\text{cm}}^2$, so $18{\text{cm}}^2$. (24 ignores the joins.)