A cone with height (h= 1 m ) and a base circle of radius ( r = 1 m) is formed from a sector- shaped sheet of paper. The sheet is of such a size and shape that its two straight edges almost touch on the sloping surface of the cone. In this state the cone is stress-free. The cone is placed on a horizontal, slippery table-top, and loaded at its apex with a vertical force of magnitude $w = 2\pi$, without collapsing. The splaying of the cone is opposed by a pair of forces of magnitude $(F)$ acting tangentially at the join in the base circle (see figure). Ignoring any frictional or bending effects in the paper, find the value of $F$
I tried to apply work energy theorem, and got $F\cdot \mathrm{d}r=w\cdot \mathrm{d}h$ but unsuccessful in proceeding further. any help will be much appreciated.