Question

a patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm if the bowl is filled with the soup of the height 4 cm how much soup the hospital has prepared daily to serve 250 patients​

Answer 1

$\large{\underline{\underline{\maltese{\red{\pmb{\sf{ \; Given \; :- }}}}}}}$

• ➳ Diameter of Bowl = 7 cm
• ➳ Height of Bowl = 4 cm

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$\large{\underline{\underline{\maltese{\green{\pmb{\sf{ \; To \; Find \; :- }}}}}}}$

• ➳ Soup prepared to serve 250 patients = ?

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$\large{\underline{\underline{\maltese{\pink{\pmb{\sf{ \; Solution \; :- }}}}}}}$

${\color{darkblue}{❒}}$ Formula Used :

${\color{cyan}{\bigstar}} \; {\underline{\boxed{\purple{\sf{ Volume{\small_{(Cylinder)}} = \pi {r}^{2} h }}}}}$

Where :

• $\rightarrowtail$ ${\sf{ \pi = \dfrac{22}{7} }}$
• $\rightarrowtail$ r = Radius
• $\rightarrowtail$ h = Height

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${\color{darkblue}{❒}}$ Calculating the Volume of 1 Bowl :

$\begin{gathered} \; \dashrightarrow \; \; \sf { Volume = \pi {r}^{2} h } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume =\dfrac{22}{7} \times \bigg\lgroup { \dfrac{Diameter}{2} } \bigg\rgroup ^{2} \times 4 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume =\dfrac{22}{7} \times \bigg\lgroup { \dfrac{7}{2} }\bigg\rgroup ^{2} \times 4 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume =\dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} \times 4 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume =\dfrac{\cancel{22}}{7} \times \dfrac{7}{\cancel2} \times \dfrac{7}{2} \times 4 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume =\dfrac{11}{\cancel7} \times \cancel7 \times \dfrac{7}{2} \times 4 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume = 11 \times \dfrac{7}{\cancel2} \times \cancel4 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume = 11 \times 7 \times 2 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf{ Volume = 77 \times 2 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; {\qquad{\red{\sf{ Volume{\small_{(1 \; Bowl)}} = 154 \; {cm}^{3} }}}} \\ \end{gathered}$

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${\color{darkblue}{❒}}$ Calculating the Volume of 250 Bowls :

$\begin{gathered} \; \longmapsto \; \; \sf { Volume{\small_{(250 \; Bowls)}} = Volume{\small_{(1 \; Bowl)}} \times No. \; of \; Bowls } \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \; \sf { Volume{\small_{(250 \; Bowls)}} = 154 \times 250 } \\ \end{gathered}$

$\begin{gathered} \; \longmapsto \; \; {\qquad{\green{\sf{ Volume{\small_{(250 \; Bowl)}} = 38500 \; {cm}^{3} }}}} \\ \end{gathered}$

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${\color{darkblue}{❒}}$ Calculating the Soup Prepaired :

$\begin{gathered} \; \implies \; \; \sf { Soup{\small_{(Prepaired)}} = \dfrac{Volume}{1000} } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { Soup{\small_{(Prepaired)}} = \dfrac{38500}{1000} } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { Soup{\small_{(Prepaired)}} = \cancel\dfrac{38500}{1000} } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; {\qquad{\pink{\sf{ Soup \; Prepared = 38.5 \; Litres }}}} \\ \end{gathered}$

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${\color{darkblue}{❒}}$ Therefore :

❛❛ Soup Prepaired for the patients is 38.5 Litres . ❜❜

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Answer 2

Answer:

Given :

• Dimeter of cylindrical bowl = 7 cm.
• Height of cylindrical bowl = 4 cm.

To Find :

• Quantity of soup to serve 250 Patients.

Using Formulas :

Let us know the required formulas before solving the question :

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \boxed{\begin{array}{l}\twoheadrightarrow\: \: \rm{Radius = \dfrac{Diameter}{2}} \\ \\ \twoheadrightarrow \rm{Volume_{(Cylinder)} = \pi{r}^{2}h}\\ \\ \twoheadrightarrow \rm{1 \:{cm}^{3} = \dfrac{1}{1000} \: litre} \end {array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Solution

Finding the radius of bowl by substituting the values in the formula :

$\begin{gathered}\qquad{\implies{Radius = \dfrac{Diameter}{2}}} \\ \\ \qquad{\implies{Radius = \dfrac{7}{2}}} \\ \\ \qquad{\implies{Radius = \cancel{\dfrac{7}{2}}}} \\ \\ \qquad{\implies{Radius = 3.5 \: cm}}\end{gathered}$

Hence, the radius of cylindrical bowl is 3.5 cm.

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Finding, the volume of cylindrical bowl by substituting the values in the formula :

$\begin{gathered} \quad{\implies{Volume_{(Cylinder)} = \pi{r}^{2}h}}\\ \\ \quad{\implies{Volume_{(Cylinder)} = \dfrac{22}{7} \times {(3.5)}^{2} \times 4}} \\ \\\quad{\implies{Volume_{(Cylinder)} = \dfrac{22}{7} \times 12.25\times 4}} \\ \\ \quad{\implies{Volume_{(Cylinder)} = \dfrac{22}{\cancel{7}} \times \cancel{12.25}\times 4}} \\ \\ \quad{\implies{Volume_{(Cylinder)} = 22 \times 1.75 \times 4}} \\ \\ \quad{\implies{Volume_{(Cylinder)} = 22 \times 7}} \\ \\ \quad{\implies{Volume_{(Cylinder)} = 154 \: {cm}^{3}}}\end{gathered}$

Hence, the volume of cylindrical bowl is 154 cm³.

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Converting the volume of cylindrical bowl 154 cm³ into litre :

$\begin{gathered} \qquad{\implies{1 \:{cm}^{3} = \dfrac{1}{1000} \: litre}} \\ \\ \qquad{\implies{154 \:{cm}^{3} = \dfrac{154}{1000} \: litre}} \\ \\ \qquad{\implies{154 \:{cm}^{3} = 0.154\: litre}} \end{gathered}$

Hence, the volume of cylindrical bowl is 0.154 litre.

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Now, finding the Quantity of soup to serve 250 Patients..

$\begin{gathered} \quad{\implies{1 \: bowl = 0.154\: litre}}\\\\\quad{\implies{250\: bowl = 0.154 \times 250}}\\\\\quad{\implies{250 \: bowl = \dfrac{154}{1000} \times 250}}\\\\\quad{\implies{250 \: bowl = \dfrac{154}{\cancel{1000}} \times \cancel{250}}}\\\\\quad{\implies{250 \: bowl = \dfrac{154}{4} \times 1}}\\\\\quad{\implies{250 \: bowl = \dfrac{154}{4}}}\\\\\quad{\implies{250\: bowl = \cancel{\dfrac{154}{4}}}}\\\\\quad{\implies{250\: bowl = 38.5 \: litre}}\end{gathered}$

Hence, 38.5 litre soup required daily to serve 250 patients.

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Learn More :

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

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