Question

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

25cm×20cm×5cm and the smaller of dimensions 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 1000cm², find the cost of cardboard required for supplying 250 boxes of each kind.


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Answer 1

Total S.A of bigger box 

=2(lb+bh+lh)

=2(25×20+25×5+20×5) cm2

=2(500+125+100)

=1450 cm2

⇒For overlapping extra area required =100450×5=72.5 cm2

∴ Total S.A (including overlaps)

=1450+72.5=1522.5 cm2

Area of cardboard sheet for 250 such boxes

=(1522.5×250) cm2

Total S.A of smaller box 

=2(15×12+15×5+12×5)cm2

=630 cm2

For overlapping area required =100630×5=31.5 cm2

Total S.A (including overlaps)=630+31.5=661.5 cm2

Area of cardboard sheet required for 250 such boxes

=250×661.5cm2=165375 cm2

Total cardboard sheet required =38062

380625+165375

=54000 cm2

⇒Cost of 1000 cm2 cardboard sheet = Rs.4

⇒Cost of 546000 cm2 cardboard sheet 

= Rs.1000546000×4

= Rs. 2184

Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

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

 

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.