Question

Make r the subject of the formula v = \pi \: h {}^{2}(r - \frac{h}{3})v=πh2(r−3h​) ​

Answer 1

Answer:

$\boxed{r = \frac{h}{3} + \frac{v}{\pi {h}^{2} } }$

Step-by-step explanation:

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