$($a$)$

$($b$)$

$($c$)$

Figure. The $3$D shape and the plan of Concordia's envisioned library, CSEC. The red inner column is built by red marble, black exterior is built by concrete and the exterior opening marked with yellow color is covered by glass. Subfigure $($a$)$ shows the bases of the cone from mid$-$surfaces to the center of the origin. The thicknesses of outer and inner cones are shown in subfigure $($c$).$

While Concordia's Board of Directors likes the design, they have a major hesitation regarding the cost of constructing this design and want to cap the structural to $$2M.$ This cost should include the price of the concrete for the exterior walls, the price of hollow marble cone column, along with the price of the glass wall. The price of concrete work is $$\frac{500}{m^3}$ of concrete and that of marble is $$7500$ per $m^3$ of stonework. Both unit prices include the labor and transportation costs. Based on Engineering Canada standards, the volume of concrete and marble works can be approximated by the area of mid$-$surface times the wall thickness. The total price for exterior glass wall can be also calculated by the unit price of $$1000$ times the glass area times its thickness; however, this price should be further regulated by multiplying to the vendor ratio that factor in the transportation and labor work, being the height of the glass surface from the crown