Solve V=1/6pih^3+1/2pi(r_1^2+r_2^2)h

$$V = \frac { 1 } { 6 } \pi h ^ { 3 } + \frac { 1 } { 2 } \pi ( r _ { 1 } ^ { 2 } + r _ { 2 } ^ { 2 } ) h$$

Solve for V

$$V=\frac{\pi h\left(3r_{1}^{2}+3r_{2}^{2}+h^{2}\right)}{6}$$

Solve for h

$$\left\{\begin{matrix}\\h=\frac{\sqrt[3]{\sqrt{\pi ^{2}\left(r_{1}^{2}+r_{2}^{2}\right)^{3}+9V^{2}}+3V}+\sqrt[3]{-\sqrt{\pi ^{2}\left(r_{1}^{2}+r_{2}^{2}\right)^{3}+9V^{2}}+3V}}{\sqrt[3]{\pi }}\text{, }&\text{unconditionally}\\h=-\sqrt[3]{\frac{\sqrt{\pi ^{2}\left(r_{1}^{2}+r_{2}^{2}\right)^{3}+9V^{2}}+3V}{\pi }}\text{, }&\left(r_{1}^{2}+r_{2}^{2}\right)^{3}+\frac{9V^{2}}{\pi ^{2}}=0\end{matrix}\right.$$