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

Video Transcription

Video Summary

The problem involves determining the fraction of volume lost when the top corner of a regular hexagonal prism is shaved off. The original prism's volume is calculated from its hexagonal base, comprising six equilateral triangles, and its height \(h\). The altered shape creates six isosceles triangular prisms, each with a specific volume expressed in terms of \(x\) and \(h\). The calculation reveals each triangular prism's volume as \(\frac{1}{12} x^2 \sqrt{3} h\). Multiplying by six (for all triangular prisms), the fraction of the original volume lost is \(\frac{1}{12}\), simplifying the ratios, leading to this result.

Keywords

hexagonal prism

volume loss

isosceles triangular prism

fraction of volume

geometry problem