Question

A cylinder has a surface area of $1850$ square meters and a radius of $9$ meters. Estimate the volume of the cylinder to the nearest whole number.

Answer 1

Step-1: Find height of the cylinder:

Surface area of cylinder $=2\mathrm{\pi rh}$

$$\begin{gathered} 1850=2\times \mathrm{\pi }\times 9\times \mathrm{h} \\ \Rightarrow \frac{1850}{18\mathrm{\pi }}=\mathrm{h}\left[\because \pi =3.14\right] \\ \Rightarrow 32.73=\mathrm{h} \end{gathered}$$

Step 2: Volume of the cylinder :

Volume of the cylinder$={\mathrm{\pi r}}^2\mathrm{h}$

$$\begin{gathered} =\mathrm{\pi }{\left(9\right)}^2(32.73) \\ =2651.13\mathrm{\pi } \end{gathered}$$

$=8234.5m^3$

Hence,the volume is about $8234.5m^3$