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 $25cm\times 20cm\times 5cm$ cm and the smaller of dimensions $15cm\times 12cm\times 5cm$ cm.For all the overlaps, $5$% of the total surface area is required extra. If the cost of the cardboard is $4$ for $1000c{m}^2$. find the cost of cardboard required for supplying $250$ boxes of each kind.

Answer 1

Total surface area of bigger box

$l=25cm$ $b=20cm$ $h=5cm$

$=2(lb+bh+lh)$

$\begin{array}{c}=2\left[25\times 20+20\times 5+25\times 5\right]\\ =2\left[500+100+125\right]\\ =1450c{m}^2\end{array}$

Extra required area $=\frac{5}{100}\times 1450$

$=72.5c{m}^2$

Total area required for $1$ bigger box $=1450+72.5$

$=1522.5c{m}^2$

Total area required for $250$ box $=1522.5\times 250$

$=380625c{m}^2$

for smaller box $l=15,b=12,h=5$

Total surface area $=2\left[15\times 12+15\times 5+12\times 5\right]$

$=630c{m}^2$

Total area required for $1$ smallest box $=630+\frac{5}{100}\times 630$

$=661.5c{m}^2$

Area of card board theet for $250$ smaller boxes $=250\times 661.5=165375c{m}^2$

Total cardboard sheet required $=380625+165375$

$=546000c{m}^2$

Cost of $546000m^2$ cardboard sheet $=Rs,\frac{546000}{1000}\times 4$

$=Rs.2184$

Therefore,

The cost of cardboard sheet $=Rs.2184$