Question

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 1

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)

= 5/100 x 1558 x 200

= 15580cm²

So, Total cardboard Required = 311600 + 15580

= 327180cm²

= 327180/1000 = 327.18 m²

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.