$$v=\pi h^{2}(r+\frac{h}{3})$$
$\left\{\begin{matrix}r=-\frac{h}{3}+\frac{v}{\pi h^{2}}\text{, }&h\neq 0\\r\in \mathrm{R}\text{, }&v=0\text{ and }h=0\end{matrix}\right.$
$$v=\pi h^{2}r+\pi h^{2}\times \frac{h}{3}$$
$$v=\pi h^{2}r+\frac{\pi h}{3}h^{2}$$
$$v=\pi h^{2}r+\frac{\pi hh^{2}}{3}$$
$$\pi h^{2}r+\frac{\pi hh^{2}}{3}=v$$
$$\pi h^{2}r+\frac{\pi h^{3}}{3}=v$$
$$\pi h^{2}r=v-\frac{\pi h^{3}}{3}$$
$$3\pi h^{2}r=3v-\pi h^{3}$$
$$\frac{3\pi h^{2}r}{3\pi h^{2}}=\frac{3v-\pi h^{3}}{3\pi h^{2}}$$
$$r=\frac{3v-\pi h^{3}}{3\pi h^{2}}$$
$$r=-\frac{h}{3}+\frac{v}{\pi h^{2}}$$
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