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

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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?

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-5 | Question 6

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.