Question Number 18556 by aplus last updated on 24/Jul/17
Answered by Tinkutara last updated on 25/Jul/17
$$\mathrm{V}\:=\:\pi{r}^{\mathrm{2}} {h} \\ $$$$\mathrm{Total}\:\mathrm{surface}\:\mathrm{area},\:{A}\:=\:\mathrm{2}\pi{r}^{\mathrm{2}} \:+\:\mathrm{2}\pi{rh} \\ $$$$=\:\mathrm{2}\pi{r}^{\mathrm{2}} \:+\:\mathrm{2}\frac{\pi{r}^{\mathrm{2}} {h}}{{r}}\:=\:\mathrm{2}\pi{r}^{\mathrm{2}} \:+\:\frac{\mathrm{2}{V}}{{r}} \\ $$$$\mathrm{Now}\:{V}\:=\:\frac{\pi}{\mathrm{4}}\:\mathrm{m}^{\mathrm{3}} \\ $$$$\frac{{dA}}{{dr}}\:=\:\mathrm{4}\pi{r}\:−\:\frac{\pi}{\mathrm{2}{r}^{\mathrm{2}} }\:=\:\mathrm{0} \\ $$$$\mathrm{8}{r}^{\mathrm{3}} \:=\:\mathrm{1}\:\Rightarrow\:{r}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{m} \\ $$