1. The problem statement, all variables and given/known data You have been employed but(sic) the Mathematics Football League (MFL) to design a football. Using the volume of revolution technique, your football design must have a capacity of 5L ± 100mL. You must present a statement considering the brief below. Just a quick side note, I have checked and it cannot be spherical, it must be in the normal elliptical rugby or gridiron shaped ball (roughly). Brief: The volume of revolution technique is to be used The football must have a capacity of 5L ± 100mL You should use a single non-linear function You must explain carefully all the steps that you take in choosing the function and the dimensions of the football You may use numerical methods (trapezium rule, numerical integration or a graphing package) in the design of the football 2. Relevant equations V=π∫[f(x)]^2 dx (from a to b) -> Sorry I don't know how to add the boundaries in properly V=π∫[f(x)-g(x)]^2 dx (from a to b) V=π∫[f(y)]^2 (from a to b - along the y-axis) x(turning point)=-b/2a T=2π/b Quadratic Formula y=ax^2+bx+c y=sin(x) etc. 3. The attempt at a solution Here's some of my attempts at the solution. (I have done it in a million different ways and cannot seem to get it, I either got somewhere between 2000 and 4500mL and 6000-7000mL. Most of my working is just me picking up small errors in the calculations. The processes in the photos are pretty much the different processes I attempted the solution with) Sorry for the bad camera, thanks in advance.