Question

The size of the matchbox is \[4cm \times 2.5cm \times 1.5cm\]. What is the volume of the packet containing \[144\] matchboxes? How many such packets can be placed in cartons of size \[1.5cm \times 84cm \times 60cm\]?

Answer 1

Hint: In order to calculate the volume of the packet, we first calculate the volume of a single match box according to the dimensions given in the question. We can get the answer afterwards by multiplying the number of match boxes.
To find the packets to be placed in a carton, we can find the volume of the carton and divide it by the volume of total packets.
Volume of the matchbox can be calculated by the formula, \[V = lbh\].

Complete step by step solution:
The matchbox is in the shape of a rectangular cuboid and three dimensional. The formula to find the volume of cuboid is:
\[V = lbh\]
Where \[l\], \[b\] and \[h\] refers to length, breadth and height respectively.
The size of the matchbox is \[4cm \times 2.5cm \times 1.5cm\] which is given. It refers to the length, breadth and height.
Applying the formula, we get,
\[V = 4 \times 2.5 \times 1.5\]
\[V = 15c{m^3}\]
Now the volume of the \[144\] matchboxes will be volume of single match box multiplied by number of packets, that is –
 \[V = 144 \times 15\]
\[V = 2160c{m^3}\]
Thus, the volume of \[144\] matchboxes is \[2160c{m^3}\].
Now the Volume of carton with dimension \[1.5cm \times 84cm \times 60cm\] will be:
\[V = 1.5 \times 84 \times 60\]
 \[V = 756000c{m^3}\]
Therefore, total number of packets that can be placed in the carton will be:
\[ = \dfrac{{Volume\,of\,carton}}{{Volume\,of\,packet}} = \dfrac{{756000c{m^3}}}{{2160c{m^3}}}\]
\[ = 350\]
Thus, \[350\] packets can be placed in the carton of dimension \[1.5cm \times 84cm \times 60cm\].
So, the correct answer is “350”.

Note: In order to solve such a type of question, the key is to find a volume of a single quantity.
We can find the volume for any number of quantities afterwards.
Identifying the shape of the matchbox and formula for volume is the key step in this question.
Point to remember is that volume is always expressed in cubic units.