Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Video Summary

The problem involves assembling \(n^3\) small cubes to create a large cube, then painting its entire outer surface. The goal is to determine the value of \(n\) when the number of small cubes with one painted face equals those with no painted faces. On each face, \( (n-2)^2 \) cubes have one face painted, totaling \(6(n-2)^2\) for the large cube. Within the cube's interior, \( (n-2)^3 \) cubes remain unpainted. Solving the equation \( 6(n-2)^2 = (n-2)^3 \) results in \( n = 8 \). Thus, the integer value of \( n \) is 8.

Keywords

cube assembly

painted cubes

unpainted cubes

equation solving

integer value n