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

## 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?

## 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.