Date: Mar 7, 2013 5:03 AM
Subject: REALLY HARD CALCULUS MODELLING AND PROBLEM SOLVING QUESTION
A light-weight "pop-up" tent consists of six flexible plastic struts that are inserted into pockets sewn into the joins of the fabric panels. The resulting shape has hexagonal horizontal cross-sections, while vertical cross-sections through the centre are semi-circular.
Derive a formula for the volume of the tent as a function of its height.
How do i do it? I tried doing a symmetrical trapezium on the graph and revolved it around half way to get the tent look, not a sphere, but the top part (the roof of the tent) was in the shape of a trapezium (shaped like a diamond? like theres edges), not half a sphere like it should be, and the base being a hexagon. If you can imagine it? Anyways, need help!