Question

Shanti Sweet Stall was placing an order for making carboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions `25cm xx20cm xx5cm` and the smaller of dimensions `15cm xx 12cm xx5cm`. For all the overlaps, 5% of the total surface area is required extra. If the cost of the carboard is Rs. 4 for `1000 cm^(2)`, find the cost of carboard required for supplying 250 boxes of each kind.

Answer 1

Dimension for bigger box, l = 25 cm, b = 20 cm and h = 5 cm
Total surface area of the bigger size bos `=2(l xx b+b xx h+h xxl)`
`=2(25xx20+20xx5+5xx25)cm^(2)`
`=2(500+100+125)cm^(2)`
`=2(725)cm^(2)=1450 cm^(2)`
Dimension for smaller box, l = 15 cm, b = 12 cm and h = 5 cm
Total surface area of the smaller size box `=2(15xx12+12xx5+5xx15)`
`=2(180+60+75)cm^(2)=2(315)cm^(2)=630 cm^(2)`
Area for all the overlaps `=5%xx(1450+630)cm^(2)=(5)/(100)xx2080 cm^(2)=104 cm^(2)`
Total surface area of both boxes and area of overlaps `=(2080+104)cm^(2)=2184 cm^(2)`
Total surface area for 250 boxes `= 2184xx250 cm^(2)`
Cost of the cardboard for `1 cm^(2)= Rs. (4)/(1000)`
Cost of the cardboard for `2184xx250 cm^(2)= Rs. (4xx2184xx250)/(1000)=Rs. 2184`