Review question

When is the area of a face of this pyramid a minimum? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6820

Question

A pyramid of given volume $V$ stands on a horizontal square base of edge $2x$, and its vertex is vertically above the centre of the base. Show that the area $A$ of a sloping triangular face is given by $A^2=\frac{9V^2}{16x^2}+x^4,$ and prove that, as $x$ varies, $A$ is least when the face is equilateral.