Question

A cube having a side of 6 cm is painted red on all the faces and then cut into smaller cubes of 1 cm

each. How many smaller cubes will have at least two faces painted?​

Answer 1

56 cubes will have at least two faces painted

Step-by-step explanation:

A cube having a side of 6 cm is painted red on all the faces and then cut into smaller cubes of 1 cm

=> number of cubes its cut =  6 * 6 * 6 / ( 1 * 1 * 1)  = 216

216 cubes

all the cubes across Edge line will have cubes two or three faces Painted

Three are 12 Edges

Each Edge will have 4 cubes +  2 cubes Sharing with three edges

cubes with at least two face Painted = 12 * 4 = 48

cubes with three face painted = 12 * 2 / 3 = 8

so number of cubes with at least two face Painted = 48 + 8 = 56

56 cubes will have at least two faces painted

Shortcut Formulas :

For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1,

Number of cubes with 0 side painted= (n-2)³

Number of cubes with 1 sides painted =6(n - 2)²

Number of cubes with 2 sides painted= 12(n-2)

Number of cubes with 3 sides painted= 8(always)