Question

A match box measures \[4\;cm \times {\text{ }}2.5{\text{ }}cm{\text{ }} \times 1.5{\text{ }}cm\]. What will be the volume of a packet containing 12 such match boxes?

Answer 1

Hint:
We need to calculate the volume of the packet, for that we need to first calculate the volume of a single match box with respect to the dimensions given in the question. Then, we just multiply the volume of the single match box with the quantity of the number of match boxes to determine the answer.

Complete step by step solution:
Already given in the question,
The dimensions of the match box are 4 cm, 2.5 cm, and 1.5 cm which is of a shape of a three-dimensional rectangular cuboid.
Here length = 4 cm, breadth = 2.5 cm and height = 1.5 cm.
12 such match boxes make a packet.
The formula of volume of a cuboid is given by \[V{\text{ }} = {\text{ }}l \times b \times h\], where l, b and h are the length, breadth and the height of the cuboid respectively.
Here the dimensions are 4cm, 2.5cm, and 1.5cm.
So, the volume of a single match box will be calculated as, \[V{\text{ }} = {\text{ }}4cm{\text{ }} \times {\text{ }}2.5cm{\text{ }} \times {\text{ }}1.5cm\]
\[ \Rightarrow V{\text{ }} = {\text{ }}15{\text{ }}cubic{\text{ }}centimetres = 15\;c{m^3}\].
Now the volume of the packet is defined as the volume of 12 such match boxes.
\[Volume{\text{ }}of{\text{ }}the{\text{ }}packet{\text{ }} = {\text{ }}12{\text{ }} \times {\text{ }}volume{\text{ }}of{\text{ }}a{\text{ }}single{\text{ }}match{\text{ }}box\]
\[ \Rightarrow Volume{\text{ }}of{\text{ }}the{\text{ }}packet{\text{ }} = {\text{ }}12{\text{ }} \times {\text{ }}15{\text{ }} = {\text{ }}180{\text{ }}cubic{\text{ }}centimetres = 180\;c{m^3}\].

Therefore, the volume of a packet containing 12 such match boxes is \[180\;c{m^3}\].

Note:
A key to solving this kind of question is to find the volume of a single quantity. After that we can just find the volume of any number of quantities by multiplying with the volume of a single unit. Here another important concept is identifying that a match box is a cuboid and utilizing its formula. Volume is always expressed in cubic units. Cubic cm is also expressed as ${\text{c}}{{\text{m}}^3}$.