Shanti sweets stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of the dimensions 25cm × 20 cm × 5 cm and the smaller of dimensions 15cm × 12cm × 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 the cardboard required for supplying 250 boxes of each kind.

# Shanti sweets stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of the dimensions 25cm × 20 cm × 5 cm and the smaller of dimensions 15cm × 12cm × 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 ${\mathit{cm}}^{2}$, find the cost of the cardboard required for supplying 250 boxes of each kind.

1. A
2. B
3. C
4. D

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### Solution:

Given: Length of big box (l) = 25 cm
Breadth of big box (b) = 20 cm
Height of the big box (h) = 5 cm
We know that,
Total surface area of cuboid = 2($\mathit{lb}+\mathit{bh}+\mathit{hl}$)
Total surface area of bigger box = 2($25×20+20×5+5×25$)
$=2\left(500+100+125\right)$

$=1450$ ${\mathit{cm}}^{2}$
Now, 5% is required for overlapping i.e., 5% of 1450
Now, Length of small box(L) = 15cm
Breadth of small box (B) = 12 cm
Height of the small box (H) = 5 cm
We know that,
Total surface area of cuboid = 2($\mathit{lb}+\mathit{bh}+\mathit{hl}$)
Total surface area of smaller box ($15×12+12×5+5×15$)
$=2\left(180+60+75\right)$
$=2\left(315\right)$
${\mathit{cm}}^{2}$
Now, 5% is required for overlapping i.e., 5% of 630 =
Thus, the total surface area of both the boxes = $1450$ ${\mathit{cm}}^{2}$ + + $630$ +

Now, total surface area of 250 such boxes
Since, the cost of = Rs 4
Cost of = Rs 4
Hence, 2 is the correct option.

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