Question

If the lateral surface of a cylinder is $94.2{\mathrm{cm}}^2$and its height is $5\mathrm{cm}$, then find (i) the radius of its base and (ii) its volume.[Use $\mathrm{\pi }=3.14$]

Answer 1

Step 1: Find the radius of the cylinder:

Given: Lateral Surface Area $=94.2{\mathrm{cm}}^2$ and height $h=5\mathrm{cm}$

Lateral Surface Area of the cylinder $=2\mathrm{\pi rh}$

$$\begin{gathered} \Rightarrow \mathrm{LSA}=2\mathrm{\pi rh} \\ \Rightarrow 94.2=2\times 3.14\times \mathrm{r}\times 5 \\ \Rightarrow \frac{94.2}{2\times 3.14\times 5}=\mathrm{r} \\ \Rightarrow 3=\mathrm{r} \end{gathered}$$

The radius of the cylinder, $r=3\mathrm{cm}$.

Step 2: Find the Volume of the cylinder:

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

$$\begin{gathered} \mathrm{Volume}={\mathrm{\pi r}}^2\mathrm{h} \\ =3.14\times {\left(3\right)}^2\times 5 \\ =141.3{\mathrm{cm}}^3 \end{gathered}$$

Hence, and radius of base $=3\mathrm{cm}$ and the volume $=141.3{\mathrm{cm}}^3$