Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets.
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 $25 \mathrm{~cm} \times 20 \mathrm{~cm} \times 5 \mathrm{~cm}$ and the smaller of dimensions $15 \mathrm{~cm} \times 12 \mathrm{~cm} \times 5 \mathrm{~cm}$. For all the overlaps, $5 \%$ of the total surface area is required extra. If the cost of the cardboard is Rs 4 for $1000 \mathrm{~cm}^{2}$, find the cost of cardboard required for supplying 250 boxes of each kind.

Solution:

Length $\left(l_{1}\right)$ of bigger box $=25 \mathrm{~cm}$

Breadth (b1) of bigger box = 20 cm

Height (h1) of bigger box = 5 cm

Total surface area of bigger box $=2(l b+/ h+b h)$

$=[2(25 \times 20+25 \times 5+20 \times 5)] \mathrm{cm}^{2}$

$=[2(500+125+100)] \mathrm{cm}^{2}$

$=1450 \mathrm{~cm}^{2}$

Extra area required for overlapping $=\left(\frac{1450 \times 5}{100}\right) \mathrm{cm}^{2}$

$=72.5 \mathrm{~cm}^{2}$

While considering all overlaps, total surface area of 1 bigger box

$=(1450+72.5) \mathrm{cm}^{2}=1522.5 \mathrm{~cm}^{2}$

Area of cardboard sheet required for 250 such bigger boxes

$=(1522.5 \times 250) \mathrm{cm}^{2}=380625 \mathrm{~cm}^{2}$

Similarly, total surface area of smaller box $=\left[2(15 \times 12+15 \times 5+12 \times 5] \mathrm{cm}^{2}\right.$

$=[2(180+75+60)] \mathrm{cm}^{2}$

$=(2 \times 315) \mathrm{cm}^{2}$

$=630 \mathrm{~cm}^{2}$

Therefore, extra area required for overlapping $=\left(\frac{630 \times 5}{100}\right) \mathrm{cm}^{2}=31.5 \mathrm{~cm}^{2}$

Total surface area of 1 smaller box while considering all overlaps

$=(630+31.5) \mathrm{cm}^{2}=661.5 \mathrm{~cm}^{2}$

Area of cardboard sheet required for 250 smaller boxes $=(250 \times 661.5) \mathrm{cm}^{2}$

$=165375 \mathrm{~cm}^{2}$

Total cardboard sheet required $=(380625+165375) \mathrm{cm}^{2}$

$=546000 \mathrm{~cm}^{2}$

Cost of $1000 \mathrm{~cm}^{2}$ cardboard sheet $=$ Rs 4

Cost of $546000 \mathrm{~cm}^{2}$ cardboard sheet $=\mathrm{Rs}\left(\frac{546000 \times 4}{1000}\right)=\mathrm{Rs} 2184$

Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be Rs 2184 .
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