Question

A closed box is made up of wood which is 1cm thick. The outer dimensions of the box is \[5cm\times 4cm\times 7cm\]. Find the volume of the wood used.

Answer 1

Hint: In this question, we have to find how much wood used to make the close box. For that first we will find the outer volume of the closed box using the dimension given in the question. Now, as wood is 1cm thick, so for the inner volume of the box, the dimension will reduce to $\left( l-2 \right),\left( b-2 \right)\ and\ \left( h-2 \right)$. Where l, b and h are outer dimensions. The volume of close box is given $=length\times breadth\times height$.

Complete step-by-step answer:
The figure shown as below. Let us consider the top view of the box to understand the inner and outer dimensions by marking the thickness.

The closed box is exactly a cuboid. So, to find the volume of a closed box we will use the formula of the volume of the cuboid.
The formula of volume of a cuboid is $=length\times breadth\times height$.
Now, the volume of wood which is used to make closed box can be found as = the volume of outer box – the volume of inner box………….(1)
We have been given the outer dimensions in the question as \[5cm\times 4cm\times 7cm\]. Therefore, we get the volume of outer box as,
The volume of outer box \[=5cm\times 4cm\times 7cm\]
\[=140c{{m}^{3}}..............\left( 2 \right)\]
Now, let us find the inner dimensions of the box. Since the thickness is 1 cm and it is present on either side of the dimensions, we have to deduct it 2 times from the outer dimensions. So, we get
The volume of inner box
 \[\begin{align}
  & =\left( 5-2 \right)\times \left( 4-2 \right)\times \left( 7-2 \right) \\
 & =3\times 2\times 5c{{m}^{3}} \\
 & =30c{{m}^{3}} \\
\end{align}\]
So, the volume of wood $=140-30$
$=110c{{m}^{3}}$

Note: The possibility of the mistake is that student may find the volume of inner box as \[\left( 5-1 \right)\times \left( 4-1 \right)\times \left( 7-1 \right)=4\times 3\times 6=72c{{m}^{2}}\] which is totally wrong. We have to remove 2cm from each of the parameters because wood is used on both sides of each parameter to make it a closed box.