Question

a cereal maker is currently packaging cereal in cylindrical boxes with a 6" diameter and a height of 10". The cereal maker is considering changing to rectangular boxes. The two boxes need to have the same height to fit on the grocery store shelf and they need to have the same volume.

Answer 1

v = pi * 36 * 10 = 360pi = 1131 in^3
Now you need a rectangular box 10" high with that volume. So, the base needs to have area 113.1 in^2

The rectangle using least material for an area is a square, so the box using least material will have a square base 10.6" square and 10" height