MathDB

Maximize the volume of the prism

Source: ISI (BS) 2007 #7

April 11, 2012

geometry3D geometryprismtrigonometrycalculuscalculus computations

Problem Statement

Consider a prism with triangular base. The total area of the three faces containing a particular vertex

A

K

. Show that the maximum possible volume of the prism is

\sqrt{\frac{K^3}{54}}

and find the height of this largest prism.