Grades 11-12 Video Solutions 2022-2022_11-12

Video Transcription

Video Summary

The original cuboid is cut into 27 smaller parts by 6 planes, each parallel and randomly distanced from a face. When considering the effect of these cuts, each face of the original cuboid effectively contributes to three separate smaller surfaces due to the intersection of planes. Through this division, each original face ends up being counted three times. Therefore, the total surface area of all the smaller cuboids combined is three times the surface area of the original cuboid. Hence, the total surface area of the 27 parts is 3S.

Keywords

cuboid

planes

surface area

division

geometry