Question

An open wooden box $80\,cm$ long, $65\,cm$ wide, and $45\,cm$ high, is made of $2.5\,cm$ thick wood.
(a) Find the capacity of the box
(b) Find the volume of wood used
(c) Weight of box
It is given that $100\,c{m^3}$ of wood weighs $8\,g$.

Answer 1

Hint: Here, in the given question, we are given that an open wooden box $80\,cm$ long, $65\,cm$ wide, and $45\,cm$ high, is made of $2.5\,cm$ thick wood and we need to find the capacity of the box, volume of wood used and weight of the box. At first, we will find the outer volume and inner volume of the wooden box (capacity of the box will be inner volume). We will subtract inner volume from outer volume to find the volume of wood used. At the end we will calculate the weight of the box using the volume of wood.

Formula used:
Volume of cuboid = length × width × height

Complete step by step answer:
Given that, outer length = $80\,cm$, outer width = $65\,cm$ and outer height = $45\,cm$.
As we know volume of cuboid = length × width × height
Therefore, outer volume of box = $80\,cm \times 65\,cm \times 45\,cm = 234000\,c{m^3}$
It is also given that, thickness of the wood = $2.5\,cm$.

Therefore, inner length = $80 - \left( {2.5 \times 2} \right) = 75\,cm$
Inner width = $65 - \left( {2.5 \times 2} \right) = 60\,cm$
Inner height = $45 - \left( {2.5} \right) = 42.5\,cm$.
Note that the thickness of wood has been subtracted twice from length and width but once from height. That is because the length and width have two sides whereas the height has only one side with the thickness of wood at the base only.

Therefore, capacity of the box = inner volume of the box = $75\,cm \times 60\,cm \times 42.5\,cm = 191250\,c{m^3}$
Hence, volume of wood used = outer volume of box – Inner volume of box
Volume of wood = $\left( {234000 - 191250} \right)\,c{m^3}$
Volume of wood = $42750\,c{m^3}$
It is also given that $100\,c{m^3}$ of wood weighs = $8g$

Therefore, weight of box = $\dfrac{8}{{100}} \times 42750 = 3420\,g$.

Note: Remember that here we are given an open box that is why we subtracted the thickness of the box once only. But if the given box was closed we would have multiplied the thickness of the base twice. We should be careful about the unit. Calculation should be done in the same unit. We should take care of the calculations so as to be sure of our final answer.