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

Video Transcription

Video Summary

To build a 3x3x3 cube with a surface exactly one-third black, grey, and white, Jill uses a total of 27 unit cubes. Each color should cover a surface area of 18 since the total surface area is 54. To minimize black cubes, she can use 6 corner cubes, achieving a surface coverage of 18. To maximize them, she uses 6 center faces, 6 edge cubes, and the hidden center cube, totaling 13 black cubes. Thus, the smallest number is 6, and the largest is 13. Consequently, the difference \( B - A \) is \( 13 - 6 = 7 \).

Keywords

3x3x3 cube

unit cubes

surface area

color distribution

difference calculation