Question

Study the following case and answer the questions based on it.

A cube with dimensions 5x5x5 is painted on all faces using a single colour. The cube is then cut into smaller sized cubes with dimensions 1x1x1.

Q. How many cubes are there where none of the faces are painted?

• A. 30
• B. 64
• C. 8
• D. 27
• E. 25

Answer 1

The correct option is D 27

N = number of cubes in a row or column
Her n = 5
Number of cubes where none of the faces are painted = $(n-2{)}^3$
$=3^3$
$=27$