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 × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 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 cm², find the cost of cardboard required for supplying 250 boxes of each kind.

Concept Used: Surface Area of Cuboid = 2(lb + bh+ hl)

Where l = length of the box

b = breadth of the box, and

h = height of the box

Given:

Length (l₁) of bigger box = 25 cm

Breadth (b₁) of bigger box = 20 cm

Height (h₁) of bigger box = 5 cm

Length of smaller box = 15 cm

Breadth of smaller box = 12 cm

Height of smaller box = 5 cm

For overlapping = 5% more of total surface area of box.

Explanation:

Total surface area of bigger box = 2(lb + lh + bh)

= [2(25 × 20 + 25 × 5 + 20 × 5)] cm²

= [2(500 + 125 + 100)] cm²

= 1450 cm²

Extra area required for overlapping

= 72.5 cm²

While considering all overlaps, total surface area of 1 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

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

= 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

Total cardboard sheet required

= (380625 + 165375) cm²

= 546000 cm²

Cost of 1000 cm² cardboard sheet = Rs 4

Cost of 546000 cm² cardboard sheet

= Rs 2184

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