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

## 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

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

**Answer:**

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]