Question

# A patient in a hospital is given soup daily in a cylindrical bowl of diameter $7cm$. If the bowl is filled with soup to a height of $4cm$. How much soup hospital has to prepare daily to serve $250$ patients?

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Solution

## Step 1: Calculate the volume of one soap:The diameter of the bowl is $D=7cm$.The radius of the bowl is $r=\frac{D}{2}$.$⇒r=\frac{7}{2}cm$.The height of the soap is $h=4cm$.The volume of a cylinder can be given by, $\mathbf{V}\mathbf{=}{\mathbf{\pi r}}^{\mathbf{2}}\mathbf{h}$.Thus the volume of the cylindrical soap is $V=\frac{22}{7}{\left(\frac{7}{2}\right)}^{2}\left(4\right)c{m}^{3}\mathbf{\left[}\mathbf{\pi }\mathbf{=}\frac{\mathbf{22}}{\mathbf{7}}\mathbf{\right]}$$⇒V=\left(\frac{22}{7}×\frac{49}{4}×4\right)c{m}^{3}\phantom{\rule{0ex}{0ex}}⇒V=22×7c{m}^{3}\phantom{\rule{0ex}{0ex}}⇒V=154c{m}^{3}$Therefore, the volume of one soap is $154c{m}^{3}$.Step 2: Calculate the total volume of the soup required dailyThe volume of soup for one patient is $154c{m}^{3}$.The total number of patients is $250$.The total volume of soup required daily is $\left(154×250\right)c{m}^{3}=38500c{m}^{3}$.Hence, the total volume of soup required daily is $38500c{m}^{3}$.

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