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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}

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