A cylinder has a surface area of 748 cm² and a radius of 7 cm. Estimate the volume of the cylinder to the nearest whole number.

Question
Solid Geometry
asked 2021-01-06
A cylinder has a surface area of 748 cm² and a radius of 7 cm. Estimate the volume of the cylinder to the nearest whole number.

Answers (1)

2021-01-07
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: \(\displaystyle{V}={490}\cdot{\left(\frac{{22}}{{7}}\right)}\)
\(\displaystyle{V}\sim{1540}{c}{m}^{{3}}\)
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