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 cm × 20cm × 5cm and the smaller of dimension 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 cardboard required for supplying 250 boxes of each kind.
Let l, b and h be the length, breadth and height of the box.
Bigger Box:
l = 25 cm
b = 20 cm
h = 5 cm
Total surface area of bigger box = 2(lb + lh + bh)
= [2(25×20+25×5+20×5)]
= [2(500+125+100)]
= 1450 cm2
Extra area required for overlapping 1450 × 5/100 cm2
= 72.5 cm2
While considering all over laps, total surface area of bigger box
= (1450 + 72.5) cm2 = 1522.5 cm2
Area of cardboard sheet required for 250 such bigger boxes
= (1522.5 × 250) cm2 = 380625 cm2
Smaller Box:
Similarly, total surface area of smaller box = [2(15 × 12 + 15 × 5 + 12 × 5)] cm2
= [2(180 + 75 + 60)] cm2
= (2 × 315) cm2
= 630 cm2
Therefore, extra area required for overlapping 630 × 5/100 cm2
= 31.5 cm2
Total surface area of 1 smaller box while considering all overlaps
= (630 + 31.5) cm2 = 661.5 cm2
Area of cardboard sheet required for 250 smaller boxes
= (250 × 661.5) cm2
= 165375 cm2
In Short:
Bigger Box:
Dimensions (in cm): l = 25, b = 20, c = 5
Total surface area (in cm2): 1450
Extra area required for overlapping (in cm2): 1450 × 5/100
= 72.5
Total surface area for all overlaps (in cm2): (1450 + 72.5) = 1522.5
Area for 250 such boxes (in cm2): (1522.5 × 250) = 380625
Smaller Box:
Dimensions (in cm): l = 15, b = 12, c = 5
Total surface area (in cm2): 630
Extra area required for overlapping (in cm2): 630 × 5/100 = 31.5
Total surface area for all overlaps (in cm2): (630 + 31.5) = 661.5
Area for 250 such boxes (in cm2): (250 × 661.5)
= 165375
Now, Total cardboard sheet required
= (380625 +165375) cm2
= 546000 cm2
Given: Cost of 1000 cm2 cardboard sheet = Rs. 4
Therefore, Cost of 546000 cm2 cardboard sheet =Rs. (546000 × 4)/1000 = Rs. 2184
Therefore, the cost of cardboard required for supplying 250 boxes of each kind will be Rs. 2184.