Ex.13.6 Q8 Surface Areas and Volumes Solution - NCERT Maths Class 9


A patient in a hospital is given soup daily in a cylindrical bowl of diameter \(7 \; \rm cm\). If the bowl is filled with soup to a height of \(4 \; \rm cm\), how much soup the hospital has to prepare daily to serve \(250\) patients?

 Video Solution
Ex exercise-13-6 | Question 8

Text Solution


Volume of cylinder \(\begin{align} = \pi {r^2}h \end{align}\). So, the amount of soup to be prepared will be the product of volume of the bowl (with \(h = 4\; \rm cm\)) and total number of patients.

What is known?

Diameter of the bowl and length of the soup, number of patients.

What is unknown?

Total soup to be prepared.


Volume of soup bowl \(= \pi {r^2}h \)

Diameter \((2R) = 7 \; \rm cm\)

Radius \((r) = \frac{7}{2}\,\,\, \rm cm \)

Height \((h) = 4\; \rm cm\)

\(\therefore \) Volume of soup in one bowl

\[\begin{align}  &= \pi {r^2}h \\ &= \frac{{22}}{7} \times \frac{7}{2} \times \frac{7}{2} \times 4\\ &= 154\,\, \rm cm^3 \end{align}\]

Volume of soup for \(1\) patient \( = 154\,\, \rm cm^3 \)

Volume of soup for \(250\) patients

\[\begin{align} &= 154 \times 250\\ & = 38500\,\, \rm cm^3 \end{align}\]


Volume of soup to be prepared for \(250\) patients is

\(\begin{align} = 38500\,\, \rm cm^3 \end{align}\) or \(38.5\) litres [as \(1000\) \( \rm cm^3 \) \(= 1\) litre]

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