Question

Make r the subject of the formula

`v = \pi \: h {}^(2)(r - (h)/(3))`
​

Answer 1

`\boxed{r = (h)/(3) + \frac{v}{\pi {h}^(2) } }`

Explanation:

`Solve \: for \: r: \\ = > v= \pi {h}^(2)(r - (h)/(3) ) \\ \\ v=\pi {h}^(2)(r - (h)/(3) )is \: equivalent \: to \: {h}^(2)\pi(r - (h)/(3) ) = v: \\ = > {h}^(2)\pi(r - (h)/(3) ) = v \\ \\ Divide \: both \: sides \: by \: \pi {h}^(2) : \\ = > r - (h)/(3) = \frac{v}{\pi {h}^(2) } \\ \\ Add \: (h)/(3) \: to \: both \: sides: \\ = > r = (h)/(3) + \frac{v}{\pi {h}^(2) }`