Find the volume of a cylinder which is formed by revolving plastic sheet of dimensions $14\ cm\times7\ cm\ ( as\ shown\ in\ figure)$ along $( i)\ AB$ and $( ii)\ BC$."

Given: A cylinder is formed by revolving plastic sheet of dimensions $14\ cm\times7\ cm\ ( as\ shown\ in\ figure)$. 

To do: To find the volume of the cylinder when the plastic sheet is revolved along:  $( i)\ AB$ and $( ii)\ BC$.

Solution:

$( i)$. When the plastic sheet is revolved along $AB$:

Height of the cylinder$( h)=7\ cm$

$AB$ becomes perimeter$( circumference)$ of the cylinder. Let $r$ be the radius of the cylinder. 

$\Rightarrow 2\pi r=14$

$\Rightarrow r=\frac{14}{2\pi}$

$\Rightarrow r=\frac{7}{\pi}$

$\therefore$ Volume of the cylinder $V=\pi r^2 h$

$\Rightarrow V=\pi\times ( \frac{7}{\pi})^2\times7$

$\Rightarrow V=\pi\times \frac{7\times7}{\pi\times\pi}\times7$

$\Rightarrow V=\frac{7\times7\times7}{\frac{22}{7}}$

$\Rightarrow V=109.09\ cm^3$

$( ii)$.  When the plastic sheet is revolved along $BC$

$AB$ is the height for the cylinder. $CD$ is the perimeter $( circumference)$ of the cylinder.

$\Rightarrow 2\pi r=7$

$\Rightarrow r=\frac{7}{2\pi}$

Volume of the new cylinder $V=\pi r^2 h$

$\Rightarrow V=\pi\times( \frac{7}{2\pi})^2\times14$

$\Rightarrow V=\pi \times \frac{7\times7}{2\times2\times\pi\times\pi}\times14$

$\Rightarrow V=\frac{7\times7\times7\times7}{2\times22}$

$\Rightarrow V=54.19\ cm^3$

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Updated on: 10-Oct-2022

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