Question

A tea packet measures $10\;{\rm{cm}} \times 6\;{\rm{cm}} \times 4\;{\rm{cm}}$. How much such packet can be placed in a cardboard box of dimensions $50\;{\rm{cm}} \times 30\;{\rm{cm}} \times 0.2\;{\rm{m}}$?

Answer 1

Hint: Find the volumes of both the tea packet and the cardboard box by using the formula for volume. The formula for volume is length $ \times $ breadth $ \times $ height. After that divide the volume of the cardboard box by the volume of the tea packet.

Complete step by step answer:
Given, the measurement of the tea packet
 $ = 10\;{\rm{cm}} \times 6\;{\rm{cm}} \times 4\;{\rm{cm}}$
It implies that the height, length and the breadth of the tea packet are $10\;{\rm{cm}}$, $6\;{\rm{cm}}$, and $4\;{\rm{cm}}$ respectively.
Step I: Now we have to find the volume of the tea packet.
We know that, the formula for volume is length $ \times $ breadth $ \times $ height.
Therefore, the volume of the tea packet
 $\begin{array}{c} = 10\;{\rm{cm}} \times 6\;{\rm{cm}} \times 4\;{\rm{cm}}\\ = {\rm{240}}\;{\rm{c}}{{\rm{m}}^3}\end{array}$
Step II: Again, the dimension of the cardboard is given as
$50\;{\rm{cm}} \times 30\;{\rm{cm}} \times 0.2\;{\rm{m}}$
It implies that the height, length and the breadth of the cardboard are $50\;{\rm{cm}}$, $30\;{\rm{cm}}$, and $0.2\;{\rm{m}}$ respectively.
Now convert the unit metre to centimetre.
We know that,
 ${\rm{1}}\;{\rm{m}} = {\rm{100}}\;{\rm{cm}}$
Therefore,
${\rm{0}}{\rm{.2}}\;{\rm{m}} = {\rm{20}}\;{\rm{cm}}$.
Hence, the dimension of the cardboard is
 $50\;{\rm{cm}} \times 30\;{\rm{cm}} \times 20\;{\rm{cm}}$
Therefore, the volume of the cardboard
 $\begin{array}{c} = 50\;{\rm{cm}} \times 30\;{\rm{cm}} \times 20\;{\rm{cm}}\\ = {\rm{30000}}\;{\rm{c}}{{\rm{m}}^3}\end{array}$
Step III: In order to find the number of tea packets that can be stored in the cardboard, we divide the volume of the cardboard box by the volume of the tea packet.
Therefore, Number of packets
$\begin{array}{c} = \dfrac{{{\rm{Volume}}\;{\rm{of}}\;{\rm{cardboard}}\;{\rm{box}}}}{{{\rm{Volume}}\;{\rm{of}}\;{\rm{a}}\;{\rm{tea}}\;{\rm{packet}}}}\\ = \dfrac{{30000\;{\rm{c}}{{\rm{m}}^3}}}{{240\;{\rm{c}}{{\rm{m}}^3}}}\\ = 125\end{array}$

Hence, the required number of tea packets that can be stored in the cardboard is $125$.

Note: Volume: Volume is the amount of three-dimensional space surrounded by a closed structure, for example the area filled or formed by a material or structure. Volume is frequently measured mathematically using the derived SI unit, the cubic meter.
In step I and step II, we measure the volume of the tea packet and the cardboard box by using the formula length $ \times $ breadth $ \times $ height.
In step III, we divide the volume of the cardboard box by the volume of the tea packet, in order to find the number of tea packets that can be stored in the cardboard.