The surface area of a cylinder with radius r and height h is given by:
\(\displaystyle{S}={2}π{r}{h}+{2}π{r}^{{2}}\)

Solve for h given that \(\displaystyle{S}={748}{c}{m}^{{2}}\) and r=7cm:

\(\displaystyle{748}={2}π{\left({7}\right)}{h}+{2}π{\left({7}\right)}^{{2}}\)

\(\displaystyle{748}={14}π{h}+{98}π\)

\(\displaystyle{748}-{98}π={14}π{h}\)

\(\displaystyle\frac{{{748}-{98}π}}{{14}}π={h}\)

Using \(\displaystyleπ\sim\frac{{22}}{{7}}\), we have: \(\displaystyle\frac{{{748}-{98}{\left(\frac{{22}}{{7}}\right)}}}{{{14}{\left(\frac{{22}}{{7}}\right)}}}={h}\)

\(\displaystyle\frac{{{748}-{308}}}{{44}}={h}\)

\(\displaystyle\frac{{440}}{{44}}={h}\)

\(\displaystyle{h}\sim{10}{c}{m}\)

The volume of a cylinder with radius r and height h is given by: \(\displaystyle{V}=π{r}^{{2}}{h}\)

\(\displaystyle{V}=π{\left({7}\right)}^{{2}}{\left({10}\right)}\)

\(\displaystyle{V}={490}π\)

Using π~22/7ZSK, we have: \(\displaystyle{V}={490}\cdot{\left(\frac{{22}}{{7}}\right)}\)

\(\displaystyle{V}\sim{1540}{c}{m}^{{3}}\)

Solve for h given that \(\displaystyle{S}={748}{c}{m}^{{2}}\) and r=7cm:

\(\displaystyle{748}={2}π{\left({7}\right)}{h}+{2}π{\left({7}\right)}^{{2}}\)

\(\displaystyle{748}={14}π{h}+{98}π\)

\(\displaystyle{748}-{98}π={14}π{h}\)

\(\displaystyle\frac{{{748}-{98}π}}{{14}}π={h}\)

Using \(\displaystyleπ\sim\frac{{22}}{{7}}\), we have: \(\displaystyle\frac{{{748}-{98}{\left(\frac{{22}}{{7}}\right)}}}{{{14}{\left(\frac{{22}}{{7}}\right)}}}={h}\)

\(\displaystyle\frac{{{748}-{308}}}{{44}}={h}\)

\(\displaystyle\frac{{440}}{{44}}={h}\)

\(\displaystyle{h}\sim{10}{c}{m}\)

The volume of a cylinder with radius r and height h is given by: \(\displaystyle{V}=π{r}^{{2}}{h}\)

\(\displaystyle{V}=π{\left({7}\right)}^{{2}}{\left({10}\right)}\)

\(\displaystyle{V}={490}π\)

Using π~22/7ZSK, we have: \(\displaystyle{V}={490}\cdot{\left(\frac{{22}}{{7}}\right)}\)

\(\displaystyle{V}\sim{1540}{c}{m}^{{3}}\)