# 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
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.

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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