Question

The circumference of the base of a cylinder vessel is 132 cm and it's height is 25 cm. Find the volume of the cylinder.

Answer 1

Step 1: Given information.

Circumference of the base of a cylinder vessel$=132\mathrm{cm}$

height of the cylinder$=25\mathrm{cm}$

Step 2: Find the radius of the cylinder.

Circumference of the base of a cylinder of radius $r$ is,

$$\begin{gathered} \mathrm{Circumference}=2\mathrm{\pi }r \\ \mathit{\Rightarrow }\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}132=2\times \frac{22}{7}\times r \\ \mathit{\Rightarrow }\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}r=\frac{132\times 7}{22\times 2} \\ \therefore r=21\mathrm{cm} \end{gathered}$$

Step 3: Find the volume of the cylinder.

The volume of the cylinder of radius $r$ and height $h$ is given by,

$$\begin{gathered} V=\mathrm{\pi }{r}^{\mathit{2}}h \\ \mathit{}\mathit{}=\frac{22}{7}\times {21}^2\times 25\left(\mathrm{radius}\mathit{,}\mathit{}r=\mathit{3}\mathit{}\mathrm{cm}\right) \\ \mathit{}\mathit{}=\frac{22}{7}\times 21\times 21\times 25 \\ =34650{\mathrm{cm}}^3 \end{gathered}$$

Therefore, the volume of the cylinder is $34650{\mathrm{cm}}^3$.