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# 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. Q.7

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What are the different way for solving the question for class 9th question of surface areas and volumes chapter of math of question no.7 of math please suggest me the best way for solving this question of exercise 13.1 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.

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1. 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 cm^2) Total surface area for all overlaps (in cm 2) Area for 250 such boxes (in cm2) Bigger Box l = 25b = 20 c = 5 1450 1450×5/100= 72.5 (1450+72.5) = 1522.5 (1522.5×250) = 380625 Smaller Box l = 15b = 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.

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