Question

How many cubic centimetres of iron is required to construct an open box whose external dimensions are $36cm$, $25cm$ and $16.5cm$ provided the thickness of the iron is $1.5cm$. If one cubic cm of iron weighs $7.5\mathrm{g}$, find the weight of the box.

Answer 1

Step $1:$ Find the required volume of iron.

Give that, $l=36cm,b=25cm$ and $h=16.5cm$

Find the external volume $V$ of the box:

$$\begin{gathered} V=36\times 25\times 16.5 \\ \Rightarrow V=14850 \end{gathered}$$ {Since, the box is open from the top.}

Therefore, the external volume $V$ of the box is $14850c{m}^3$.

Internal dimensions of the box:

$$\begin{gathered} l\text{'}=36-2(1.5) \\ \Rightarrow l\text{'}=33cm \end{gathered}$$

Similarly,

$$\begin{gathered} b\text{'}=25-2(1.5) \\ \Rightarrow b\text{'}=22cm \end{gathered}$$

And,

$\begin{array}{rcl}h\text{'}& =& 16.5-1.5\\ & \Rightarrow & h\text{'}=15cm\end{array}$ {Since, the box is open from the top.}

Now, find the internal volume $V\text{'}$ of the box:

$$\begin{gathered} V\text{'}=33·22·15 \\ \Rightarrow V\text{'}=10890 \end{gathered}$$

Therefore, the internal volume $V\text{'}$ of the box is $10890c{m}^3$.

Find the volume of the iron used to construct the given box as follows:

$\begin{array}{rcl}{V}_I& =& V-V\text{'}\\ & \Rightarrow & V_I=14850-10890\\ & \Rightarrow & V_I=3960\end{array}$

Therefore, $3960c{m}^3$ of iron is required to construct given box.

Step $2:$ Compute the weight of the box.

Since, it is given that $1c{m}^3$ of iron weighs $7.5\mathrm{g}$.

Therefore, the weight $w$ of the box is given by:

$$\begin{gathered} w=3960\times \left(7.5\right) \\ \Rightarrow w=29700 \end{gathered}$$

Therefore, the weight of the box is $29700g$ or $29.7kg$.