Quandaries and Queries 

Question: I am building a model for my architecture class. I need to build a elliptic cone out of chipboard and i have no idea how to do this. The cone needs to be 20in tall and the ellipse has a max radius of 10in and a min radius of 8in. So my question is how do i lay this out on a piece of paper so that i can form the cone after i cut it out. Thanks Ben Hi Ben, If the instructions are to build an elliptic cone I wouldn't take an algebraic approach, I would build one. To construct a circular cone that is 20 inches tall and has a base radius of 10 inches you need a sector of a circle with angle ^{2pi}/_{root(5)} radians and the radius of the circle 10 root(5) inches. Cut a segment with this center angle and a radius a little larger than 10 root(5) inches. Form it into a circular cone. On another piece of cardboard cut an elliptic hole the size you describe, "a max radius of 10in and a min radius of 8in". Place the cone on a table with the circular base on the table and slide the elliptic hole over the cone, keeping the ellipse parallel to the table top, distorting the circle, until it won't go down any further. With a pencil trace the elliptic shape onto the cone. Disassemble the cone, cut along the line you just drew and then reassemble the cone. I hope this makes sense,Penny 

