# A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

May 13, 2016

$54$ one cubic centimeter cubes will have exactly one of their sides painted.
There are six sides of the cube and as side of cube is $5$ cm and hence each side will have $5 \times 5 = 25$ one cubic centimeter cubes painted.
However, all the cubes on sides and corners will have painted sides more than one as they share with adjoining sides and only $3 \times 3 = 9$ one cubic centimeter cubes will have one side painted.
As there are six sides, $9 \times 6 = 54$ one cubic centimeter cubes will have exactly one of their sides painted.