Question

The circumference of the base of cylindrical vessel is $132cm$ and its height is $25cm$. How many litres of water can it hold? $\left(1000c{m}^3=1L\right)$ (Assume $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Step 1: Find the radius

Given,

Circumference of the base of a cylindrical vessel $=132cm$

Height of vessel, $h=25cm$

The base of the cylinder is of a circle shape,

circumference $=2\mathrm{\pi r}$ ($r$ is the radius)

$$\begin{gathered} 2\mathrm{\pi r}=132 \\ \mathrm{r}=\frac{132}{2\mathrm{\pi }} \\ \mathrm{r}=66\times \frac{7}{22} \\ \mathrm{r}=21\mathrm{cm} \end{gathered}$$

Radius is $21cm$.

Step 2: Find the capacity

The volume of a cylinder $=2\mathrm{\pi rh}$

$$\begin{gathered} =2\times \frac{22}{7}\times 21\times 21\times 25 \\ =485100c{m}^3 \end{gathered}$$

Therefore, volume is $485100c{m}^3$

We know that, $1000c{m}^3=1L$

So, Volume $=\frac{485100}{1000L}=485.1L$

Therefore, the vessel can hold $485.1litres$ of water.