Question

A godown measures 40m x 25m x 15m. Find the maximum number of wooden crates each measuring 1.5m x 1.25m x 0.5m that can be stored in the godown.

Answer 1

Hint: Apply the unitary method. Number of boxes could be equal to the volume of godown / volume of the box. So find the volume of godown and then find the volume of the box. Then we just need to divide both the quantities and we will get the required answer.

Complete step-by-step answer:
Dimensions of godown = 40m x 25m x 15m.
Dimensions of wooden box = 1.5m x 1.25m x 0.5m.
The box and the godown are cuboids.
Volume of a cuboid = length x breadth x height
Volume of the godown $=\left( 40\times 25\times 15 \right){{m}^{3}}$
$=15,000{{m}^{3}}$
Volume of the box $=\left( 1.5\times 1.25\times 0.5 \right){{m}^{3}}$
$=0.9375{{m}^{3}}$
We now use the unitary method to find the number of boxes.
1 box occupies $0.9375{{m}^{3}}$.
Then, let x boxes occupy $15,000{{m}^{3}}$.
$\begin{align}
  & \Rightarrow x=\dfrac{15000}{0.9375} \\
 & =16000 \\
\end{align}$
Answer is 16000 boxes.


Note: While performing calculations involving units, make sure to maintain uniformity of units. If units are different, convert them to the same unit using conversion formulae. For example: If one length is given in metre and the other is given in centimetre, they cannot be added directly. Either convert both of them to centimetre or convert both of them to metre.