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

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## Question

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?

## Text Solution

Reasoning:

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.

Steps:

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]