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

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Solution

## 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 $\begin{array}{rcl}2\mathrm{\pi r}& =& 11\\ 2×\frac{22}{7}×\mathrm{r}& =& 11\\ \frac{44}{7}×\mathrm{r}& =& 11\\ \mathrm{r}& =& \frac{11}{44}×7\\ \mathrm{r}& =& \frac{1}{4}×7\\ \mathrm{r}& =& \frac{7}{4}\mathrm{cm}\end{array}$Height of cylinder $=$Breadth of the rectangular paper $=$$h=4cm$Volume of cylinder $={\mathrm{\pi r}}^{2}\mathrm{h}$ $=\frac{22}{7}×{\left(\frac{7}{4}\right)}^{2}×4\phantom{\rule{0ex}{0ex}}=\frac{22}{7}×\frac{7×7}{4×4}×4\phantom{\rule{0ex}{0ex}}=\frac{22}{4}×\frac{7}{7}×\frac{4}{4}×7\phantom{\rule{0ex}{0ex}}=\frac{11}{2}×\frac{1}{1}×\frac{1}{1}×7\phantom{\rule{0ex}{0ex}}=\frac{77}{2}\phantom{\rule{0ex}{0ex}}=38.5c{m}^{3}$  Suggest Corrections  10      Explore more