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.

Solution:

Let l, b and h be the length, breadth and height of the box.

Bigger Box:

l = 25cm

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:

Box	Dimensions (in cm)	Total surface area (in cm2 )	Extra area required for overlapping (in cm2)	Total surface area for all overlaps (in cm 2)	Area for 250 such boxes (in cm2)
Bigger Box	l = 25 b = 20 c = 5	1450	1450×5/100 = 72.5	(1450+72.5) = 1522.5	(1522.5×250) = 380625
Smaller Box	l = 15 b = 12 h =5	630	630×5/100 = 31.5	(630+31.5) = 661.5	( 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.