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

Answer 1

Dimensions of bigger box $=25\times 20\times 5$

Total surface area $=2(lb+bh+lh)$

$=2(25\times 20+20\times 5+25\times 5)c{m}^2$

$=1450c{m}^2$

Smaller box $=15\times 12\times 5$

T.S.A$=2(15\times 12+12\times 5+5\times 15)$

$=630c{m}^2$

T.S.A. of $250$ boxes of each type $=250(1450+630)$

$=520000c{m}^2$

Extra area required $=\frac{5}{100}\times \left(520000\right)=26000c{m}^2$

$\therefore$ Total cardboard required $=520000+26000$

$=546000c{m}^2$

Total cost $=546000\times \frac{4}{1000}$ $\Rightarrow 2184$ Rs.