A rectangular sheet of paper is rolled in two different ways to f… - Vidyadip

Question

A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures $44\ cm \times 33\ cm$.

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Answer

We have, length of the sheet $= 44\ cm$
breadth of the sheet $= 33\ cm$
Case $1$: When it is roled along its length.
Now, circumference of base of cylinder formed = length of sheet
$\Rightarrow2\pi\text{r}=44$ (where, $r$= radius of base)
$\Rightarrow2\times\frac{22}{7}\times\text{r}= 44$
$\Rightarrow\text{r}=7\text{cm}$
Now, height of the cylinder = breadth of the sheet
$\Rightarrow\text{h}=33\text{cm}$
Now, volume of cylinder $=\pi\text{r}^2\text{h}=\frac{22}{7}\times49\times33=5082\text{cm}^3$
Case $2$: When it is roled along its breadth.
Now, circumference of base of cylinder formed = breadth of sheet
$\Rightarrow2\pi\text{r}=33$ (where, $r$ = radius of base)
$\Rightarrow2\times\frac{22}{7}\times\text{r}=33$
$\Rightarrow\text{r}=\frac{21}{4}\text{cm}$
Now, height of the cylinder = length of the sheet
$\Rightarrow\text{h}=44\text{cm}$
Now, volume of cylinder $=\pi\text{r}^2\text{h}=\frac{22}{7}\times\frac{21}{4}\times\frac{21}4{}\times44=3811.5\text{cm}^3$

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