a = 2\pi R^2 + 2\pi R
2\pi R^2+2\pi Rh=a
2\pi R^2+2\pi h R-a=0
Korzystam ze wzoru ax^2+bx+c=0 i ze wzoru \Delta=b^2-4ac
\Delta=(2\pi h)^2-4\cdot 2\pi \cdot a=4\pi ^2h^2-4\cdot 2\pi a=4(\pi^2h^2-2\pi a)
\sqrt\Delta=\sqrt{4(\pi^2h^2-2\pi a)}=2\sqrt{\pi^2h^2-2\pi a}
R=\frac{-b\pm \sqrt\Delta}{2a}
R=\frac{-\not2\pi h\pm \not2\sqrt{\pi^2h^2-2\pi a}}{\not2\cdot 2\pi}
R=\frac{-\pi h\pm \sqrt{\pi^2h^2-2\pi a}}{2\pi}
R=\frac{-\pi h}{2\pi}\pm \frac{1}{2\pi}\sqrt{\pi^2 h^2-2\pi a}
R=-\frac{h}{2}\pm \frac{1}{2}\sqrt{\frac{{\pi^2 h^2-2\pi a}}{\pi^2}}
R=-\frac{1}{2}(h \pm \sqrt{h^2-\frac{2a}{\pi}})
Stąd
R_1=-\frac{1}{2}(h - \sqrt{h^2-\frac{2a}{\pi}})
R_2=-\frac{1}{2}(h + \sqrt{h^2-\frac{2a}{\pi}})