Answer:
[tex] r = \sqrt{\frac{3Q}{\pi(12 + h)}} [/tex]
Step-by-step explanation:
[tex]Q = 4\pi {r}^{2} + \frac{1}{3} \pi {r}^{2} h \\ \\ Q = {r}^{2} \bigg(4\pi + \frac{1}{3} \pi h \bigg)\\ \\ Q = {r}^{2} \pi\bigg( \frac{12}{3} + \frac{1}{3} h \bigg)\\ \\ Q = {r}^{2} \pi\bigg( \frac{12 + h}{3} \bigg)\\ \\ {r}^{2} = \frac{Q}{\pi\bigg( \frac{12 + h}{3} \bigg)} \\ \\ {r}^{2} = \frac{3Q}{\pi(12 + h)} \\ \\ r = \sqrt{\frac{3Q}{\pi(12 + h)}} [/tex]
