Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required.
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 × 20 cm × 5 cm and the smaller of dimesnsions 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.
2 Answers
For bigger boxes :
t = 25 cm, b = 20 cm, h = 5 cm
Total surface area of 1 bigger box = 2(lb + bh + hl)
= 2(25 × 20 + 20 × 5 + 5 × 25) cm2
= 2 (500 + 100 + 125) cm2 = 1450 cm2
Area of cardboard required for overlaps
= 5% of 1450 cm2 = 1450x 5 /100 × cm2 = 72.5 cm2.
Total area of cardboard needed for 1 bigger box
= (1450 + 72.5) cm2 = 1522.5 cm2
Total area of cardboard needed for 250 bigger boxes = 1522.5 × 250 cm2
= 380625 cm2.
For smaller boxes :
t = 15 cm, b = 12 cm, h = 5 cm
Total surface area of 1 smaller box = 2 (lb + bh + hl)
= 2(15 × 12 + 12 × 5 + 5 × 15) cm2
= 2 (180 + 60 + 75) cm2 = 630 cm2
Area of cardboard required for overlaps
= 5% of 630 cm2 = 630x 5 /100 × cm2 = 31.5 cm2
Total area of cardboard needed for 1 smaller box = (630 + 31.5) cm2
= 661.5 cm2
Total area of cardboard needed for 250 smaller boxes
= 661.5 × 250 cm2 = 165375 cm2
Now, total area of cardboard needed for 500 boxes (250 bigger and 250
smaller boxes) = (380625 + 165375) cm2 = 546000 cm2
Cost of 1000 cm2 of cardboard = Rs 4
∴ Cost of 546000 cm2 of cardboard = Rs 4/1000 × 546000 = Rs 2184 Ans
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
= (1450 x 5/100) 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 = (630 x 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
Total cardboard sheet required = (380625 + 165375) cm2 = 546000 cm2
Cost of 1000 cm2 cardboard sheet = Rs 4
Cost of 546000 cm2 cardboard sheet
= Rs(546000 x 4/1000) = Rs 2184
Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be Rs 2184.