A 4cm x 5cm x 7cm rectangular prism is painted on all faces. If the prism is cut into 1cm x 1cm x 1cm cubes, how many cubes do not have paint on any of its sides?

Answer 1

all the outer cubelets have paint. So, reduce the dimensions by 2 to exclude the outer faces, and the inner (paintless) solid is

2x3x5

So, 30 cubelets have no paint.