Question

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The ** 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.

Answer 1

For ** boxes :

t = 25 cm, b = 20 cm, h = 5 cm

Total surface area of 1 ** 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 ** box

= (1450 + 72.5) cm2 = 1522.5 cm2

Total area of cardboard needed for 250 ** 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 ** 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