Question

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. -Maths 9th

Answer 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 = 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.