Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions25 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
Length (l1) of bigger box = 25 cm
Breadth (b1) of bigger box = 20 cm
Height (h1) of bigger box = 5 cm
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 = (
) cm2
= 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
= (
) 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
Total cardboard sheet required
= (380625 + 165375) cm2
= 546000 cm2
Cost of 1000 cm2 cardboard sheet = Rs 4
Cost of 546000 cm2 cardboard sheet
= Rs (
)
= Rs 2184
Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be Rs 2184