# Ex.13.5 Q6 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

A village, having a population of \(4000,\) requires \(150\) litres of water per head per day. It has a tank measuring \(\rm 20 \,m × 15 \,m × 6 \,m.\) For how many days will the water of this tank last?

## Text Solution

**Reasoning:**

Capacity of the tank is the volume of cuboid.

Volume of the tank = length \(\times\) breadth \(\times\) height

**What is the known?**

Requirement of water per head per day measurements of the tank.

**What is the unknown?**

Number of days the water of the tank will last.

**Steps:**

Requirement of water per head per day \(= 150\rm\, litres.\)

Requirement of water for \(4000\) population\(\begin{align}\, = 150 \times 4000 = 600000\,l \end{align}\)

\[\begin{align}1000\,l &= 1\,\,\rm{m^3} \\\therefore 600000l &= \frac{{600000}}{{1000}} = 600\,\, \rm {m^3} \end{align}\]

length of the tank\((l) = 20\,\,\rm m\)

breadth of the tank\((b) = 15\,\,\rm m\)

height of the tank\((h) = 6\,\,\rm m\)

Capacity of the tank \(=\) Volume of the cuboid

\[\begin{align}& = l \times b \times h \\ &= 20 \times 15 \times 6 \\ &= 1800\,\, \rm {m^3} \end{align}\]

Number of days for which the water of the tank will last

\[\begin{align} & = \frac{\text{Capacity of the tank}}{\left[\begin{array}{l} {\text{Requirement of water }} \\ {\text{for the total population}} \\ \end{array} \right]} \\ & = \frac{{1800}}{{600}} \\ & = 3{\text{ days}}\end{align}\]

**Answer:**

The water of tin tank will last for \(3\) days.