Question

If V = pr²h and S = 2pr² + 2prh, then express V in terms of S, p and r.

Answer 1

V = πr²h and S = 2πr² + 2πrh
S = 2πr² + 2πrh
⇒ 2rh = S - 2πr²

⇒ h = ${\displaystyle \frac{\text{S}-2\pi {\text{r}}^2}{2\pi \text{r}}}$

Substitute h in V = πr2h

⇒ V = ${\displaystyle \pi {\text{r}}^2\left(\frac{\text{S}-2\pi {\text{r}}^2}{2\pi \text{r}}\right)}$

⇒ V = ${\displaystyle \text{r}\left(\frac{\text{S}-2\pi {\text{r}}^2}{2}\right)}$

⇒ V = ${\displaystyle \frac{\text{Sr}}{2}-\pi {\text{r}}^3}$.