Question

The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm. Find the height and the volume of the cylinder.

Answer 1

Let r be the radius and h be the height of the cylinder.
Circumference of its base(circle) = 110 cm.
$\Rightarrow 2\mathrm{\pi }r=110\Rightarrow r=\frac{110}{2\mathrm{\pi }}\Rightarrow r=\frac{110}{2\times {\displaystyle \frac{22}{7}}}\Rightarrow r=\frac{110\times 7}{2\times 22}\Rightarrow r=\frac{35}{2}\mathrm{cm}$
Curved surface area of a cylinder = 4400 cm².
$$\begin{gathered} \Rightarrow 2\mathrm{\pi }rh=4400\Rightarrow h=\frac{4400}{2\mathrm{\pi }r}\Rightarrow h=\frac{4400}{2\times {\displaystyle \frac{22}{7}}\times {\displaystyle \frac{35}{2}}} \\ \Rightarrow h=\frac{4400\times 7\times 2}{2\times 22\times 35}\Rightarrow h=40\mathrm{cm} \end{gathered}$$
Also, Volume of the cylinder = $\mathrm{\pi }{r}^{2}h=\frac{22}{7}\times {\left(\frac{35}{2}\right)}^2\times 40=\frac{22\times 35\times 35\times 40}{7\times 2\times 2}=38500{\mathrm{cm}}^3.$