Question

Make r the subject.
Q=4πr^2+1/3πr^2h


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Answer 1

`r = \sqrt{(3Q)/(\pi(12 + h))}`

Explanation:

`Q = 4\pi {r}^(2) + (1)/(3) \pi {r}^(2) h \\ \\ Q = {r}^(2) \bigg(4\pi + (1)/(3) \pi h \bigg)\\ \\ Q = {r}^(2) \pi\bigg( (12)/(3) + (1)/(3) h \bigg)\\ \\ Q = {r}^(2) \pi\bigg( (12 + h)/(3) \bigg)\\ \\ {r}^(2) = (Q)/(\pi\bigg( (12 + h)/(3) \bigg)) \\ \\ {r}^(2) = (3Q)/(\pi(12 + h)) \\ \\ r = \sqrt{(3Q)/(\pi(12 + h))}`