Question

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25cm\times 20cm\times 5cm$ and the smaller of dimension $15cm\times 12cm\times 5cm$. For all the overlaps, $5\%$ of the total surface area is required extra. If the cost of the cardboard is Rs. $4$ for $1000$ cm², find the cost of cardboard required for supplying $250$ boxes of each kind.

Answer 1

Step 1. Total surface of area of Bigger Boxes

$\begin{array}{rcl}\mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{bigger}\mathrm{cardboard}\mathrm{box}& =& 2(lb+bh+lh)\\ & =& 2(25\times 20+20\times 5+25\times 5)c{m}^2\\ & =& 2(500+100+125)c{m}^2\\ & =& 1450c{m}^2\end{array}$

Total surface area of bigger cardboard box including overlaps$=\left[1450+(0.05\times 1450)\right]$

$=1522.5c{m}^2$

Area of 250 bigger boxes $=(1522.5\times 250)c{m}^2=380625c{m}^2$

Step 2. Total surface of area of smaller boxes

$\begin{array}{rcl}\mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{smaller}\mathrm{cardboard}\mathrm{box}& =& 2(lb+bh+lh)\\ & =& 2(15\times 12+12\times 5+5\times 15)\\ & =& 2(180+60+75)\\ & =& 630c{m}^2\end{array}$

Total surface area of smaller cardboard box including overlaps$=\left[630+(0.05\times 630)\right]$

$=661.5cm2$

Area of 250 smaller boxes

$$\begin{gathered} =(661.5\times 250)c{m}^2 \\ =165375cm2 \end{gathered}$$

Total cardboard sheet required$=(380625+165375)c{m}^2=546000c{m}^2$

Step 3. Cost Calculation

Cost of $1000$ cm² Cardboard sheet = Rs. $4$ (Given)

Therefore, cost of $546000c{m}^2$ Cardboard sheet$=\frac{(546000\times 4)}{1000}=2184Rs.$

Hence, the cost of cardboard needed for providing $250$ boxes of each kind is $2184$ rupees.