Question

A solid cube, 8 inches x 8 inches x 8 inches is painted red on all the faces. the cube is then sliced into smaller equal sized cubes of 1 inch x 1 inch x 1 inch. how many of these small cubes will have exactly two red faces?

Answer 1

Find the total surface area of the cube with side 8 and then find the total surface area of smaller cube with side 1 and divide the bigger cube with smaller cube

Answer 2

Given: A solid cube, 8 inches x 8 inches x 8 inches is painted red on all the faces. the cube is then sliced into smaller equal sized cubes of 1 inch x 1 inch x 1 inch.

To find: How many of these small cubes will have exactly two red faces.

Solution: 36 of these small cubes will have exactly two red faces.

The smaller cubes that are at the corners will have three red faces. The smaller cubes that are at the edges have exactly two red faces. Now, the larger cube is 8 inches x 8 inches x 8 inches and the size of the smaller cubes is 1 inch x 1 inch x 1 inch, there are 6 smaller cubes at each edge (excluding the corner cubes.

There are 6 edges in a cube and hence, the number of cubes that have exactly 2 red faces can be calculated as shown below.

$6 edges * 6 cubes = 36 cubes$

Therefore, 36 of these small cubes will have exactly two red faces.