Question

A solid cube is painted green on two adjacent sides and black on the sides opposite to the green sides and yellow on the remaining sides. the cube is then cut into 64 small cubes of equal size. how many cubes have three sides painted?

Answer 1

8 cubes have three sides painted

Answer 2

Eight smaller cubes have their three sides painted.

Explanation:

• Here Three colors used to paint sides of a cube.
• Green is painted on two adjacent sides.
• The opposite sides of these green sides are painted black
• Remaining are two sides which are painted yellow. hence, all the six sides of the cube are painted.
• Now new small cubes are cut from this painted cube.
• For the smaller cube to have three sides painted should have its three sides be a part of bigger cubes' sides.
• Such types of cubes are only possible to be cut from the corners of the bigger cube and a cube has eight corners.
• Hence, number of cubes with three sides painted are $8$.