Q. 24.4( 13 Votes )

Cardboard boxes of two different sizes are made. The bigger has dimensions 20cm, 15cm and 5cm and the smaller dimensions 16cm, 12cm and 4cm. 5% of the total surface area is required extra for all overlaps. If the cost of the cardboard is Rs. 20 for one square metre, find the cost of the cardboard for supplying 200 boxes of each kind.

Answer :


For bigger box:


Length of the bigger box = 20cm


Breadth of the bigger box = 15cm


Height of the bigger box = 5cm


So, Total Surface Area of bigger box = 2(lb + bh + hl)


= 2(20×15 + 15×5 + 5×20)


= 2(300 + 75 + 100)


= 2(475)


= 950cm2


For Smaller box:


Length of the smaller box = 16cm


Breadth of the smaller box = 12cm


Height of the smaller box = 4cm


So, Total Surface Area of bigger box = 2(lb + bh + hl)


= 2(16×12 + 12×4 + 4×16)


= 2(192 + 48 + 64)


= 2(304)


= 608cm2


Total surface area of 200 boxes of each type = 200(950 +608)


= 200 × 1558


= 311600cm2


Extra Area Required = 5% of (950 + 608)



= 15580cm2


So, Total cardboard Required = 311600 + 15580


= 327180cm2



Cost of Cardboard for 1m2 = Rs 20


Cost of Cardboard for 327.18 m2 = 20 × 327.18


= Rs 654.36


Hence, the cost of the cardboard for supplying 200 boxes of each kind is Rs 654.36.


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