Ex.13.5 Q5 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

The capacity of a cuboidal tank is \(50000\) litres of water. Find the breadth of the tank, if its length and depth are respectively \(2.5\rm m\) and \(10\rm m.\)

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

Text Solution

Reasoning:

Capacity of the cuboidal tank \(=\) Volume of the cuboidal tank.

Volume of the cuboid \(\begin{align} = l \times b \times h \end{align}\)

What is the known?

Capacity of the tank length and height of the tank.

What is the unknown?

Breadth of the tank.

Steps:

Capacity of the tank \(= 50000\rm \,\,\ litres.\)

\[\begin{align}1000\,\,l& = 1\,\,\rm {m^3} \\50000\,l &= \frac{{50000}}{{1000}} = 50\,\,\rm{m^3} \end{align}\]

Volume has to be changed in \(\begin{align}\rm {m^3} \end{align}\) because all the measurements are in meter.

Volume of the cuboid\(\begin{align}\, = l \times b \times h \end{align}\)

length\(\,(l)\, = 2.5\,\rm cm \)

breadth\(\,(b)\,= \,? \)

height \((h) = 10\,\,\rm cm\) 

\[\begin{align}2.5 \times 10 \times b &= 50\\b &=\frac{{50}}{{2.5 \times 10}}\\ &= 2\,\,\rm m \end{align}\]

Answer:

The breadth of the cuboidal tank is \(2 \rm \,m.\)