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Ex.13.5 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

A cuboidal vessel is \(10\rm m\) long and \(8 \;\rm{ m}\) wide. How high must it be made to hold \(380\rm \,\,cubic\, metres\) of a liquid?

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-5 | Question 3

Text Solution

Reasoning:

Capacity of the cuboid vessel is the cuboid.

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

What is known?

Length and breadth of the cuboidal vessel, and the capacity of the vessel.

What is unknown?

The height of the vessel having \(\begin{align}380\,\rm{m^3} \end{align}\) capacity.

Steps:

Capacity of the cuboidal vessel\(=\)volume of the cuboid.

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

 Length \((l) = 10\,\,\rm m \)

 Breadth \((b) = 8\,\,\rm m\) 

 Volume \((V) = 380\,\,\rm c{m^3} \)

 Height\((h) = ? \)

\(\begin{align} 380 &= 10 \times 8 \times h\\ h& = \frac{{380}}{{10 \times 8}} \\&= \frac{{19}}{4} \\ &=4.75 \rm m\end{align}\)

Answer:

The cuboidal vessel must be made \(4.75 \rm m\) height.