Question

A rectangular piece of paper $11cm\times 4cm$ is folded without overlapping to make a cylinder of height $4cm$ .find the volume of the cylinder?

Answer 1

Given that,

Length of the rectangular paper$=11cm$

The breadth of the rectangular paper$=4cm$

Circumference of the circular part of the cylinder $=2\mathrm{\pi r}$

also given that the cylinder is rolled along its length

Hence Circumference of the circular part of the cylinder $=$Length of the rectangular paper

$\begin{array}{rcl}2\mathrm{\pi r}& =& 11\\ 2\times \frac{22}{7}\times \mathrm{r}& =& 11\\ \frac{44}{7}\times \mathrm{r}& =& 11\\ \mathrm{r}& =& \frac{11}{44}\times 7\\ \mathrm{r}& =& \frac{1}{4}\times 7\\ \mathrm{r}& =& \frac{7}{4}\mathrm{cm}\end{array}$

Height of cylinder $=$Breadth of the rectangular paper $=$$h=4cm$

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

$$\begin{gathered} =\frac{22}{7}\times {\left(\frac{7}{4}\right)}^2\times 4 \\ =\frac{22}{7}\times \frac{7\times 7}{4\times 4}\times 4 \\ =\frac{22}{4}\times \frac{7}{7}\times \frac{4}{4}\times 7 \\ =\frac{11}{2}\times \frac{1}{1}\times \frac{1}{1}\times 7 \\ =\frac{77}{2} \\ =38.5c{m}^3 \end{gathered}$$