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?

Answer 1

Step 1: Calculate the volume of one soap:

The diameter of the bowl is $D=7cm$.

The radius of the bowl is $r=\frac{D}{2}$.

$\Rightarrow r=\frac{7}{2}cm$.

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 $V=\frac{22}{7}{\left(\frac{7}{2}\right)}^2\left(4\right)c{m}^3\mathbf{[}\mathbf{\pi }\mathbf{=}\frac{\mathbf{22}}{\mathbf{7}}\mathbf{]}$

$$\begin{gathered} \Rightarrow V=\left(\frac{22}{7}\times \frac{49}{4}\times 4\right)c{m}^3 \\ \Rightarrow V=22\times 7c{m}^3 \\ \Rightarrow V=154c{m}^3 \end{gathered}$$

Therefore, the volume of one soap is $154c{m}^3$.

Step 2: Calculate the total volume of the soup required daily

The 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 $\left(154\times 250\right)c{m}^3=38500c{m}^3$.

Hence, the total volume of soup required daily is $38500c{m}^3$.