Question

1. a cube made of 1,331 small cubes gets a painted surface. find the number of small unpainted cubes.

Explanation:

Step1: Find side length of big cube

The volume of the big cube is 1331 (number of small cubes). Since volume of a cube is \( V = n^3 \) (where \( n \) is side length), solve \( n^3 = 1331 \). We know \( 11^3 = 1331 \), so \( n = 11 \).

Step2: Find side length of inner unpainted cube

The unpainted cubes form a smaller cube inside, with side length \( n - 2 \) (subtract 2 layers: one from each side). So \( 11 - 2 = 9 \).

Step3: Calculate volume of unpainted cube

Volume of inner cube is \( 9^3 \). \( 9^3 = 9\times9\times9 = 729 \).

Answer:

729