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 25 cm × 20 cm × 5 cm and the smaller of dimensions 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

Measurement of big box, l = 25 cm. 

b = 20 cm. 

h = 5 cm. 

∴ TSA of eacxh big box = 2(lb + bh + lh) 

= 2 [25 × 20 + 20 × 5 + 25 × 5] 

= 2 [500 + 100 + 120] 

= 2 (725) T.S.A. =1450 cm² . 

For all the overlaps 5% of the total surface area is required extra. 

\(\frac{5}{100} \times1450\)

= 72.5 cm² . 

∴ Total surface area of big box, 

TSA = 1450 + 72.5 = 1522.5 cm² . 

Area required for 1 box is 1522.5 cm² 

Area required for 25 boxes … ?… 

= 1522.5 × 250 = 380625 cm² . 

Dimension of small box, l = 15 cm. b = 12 cm. h = 5 cm. 

∴ TSA of each small box = 2(lb + bh + lh) 

= 2 [15 × 12 + 12 × 5 + 15 × 5] 

= 2 [180 + 60 + 75] = 2 × 315 

= 630 cm² . 

More area to overlap cardboard is 5% more. 

For 100 cm² , 5 cm² 

For 630 cm² , …?… = 31.5 cm² . 

∴ T.S.A.= 630 + 31.5= 661.5 cm² . 

TSA required for 1 box is 661.5 cm² 

TSA required for 250 boxes …?… = 661.5 × 250 = 165375 cm² . 

∴ To prepare 500 boxes, TSA = 380625 + 165375 = 546000 cm² . 

Cost of 1000 sq.cm, of cardboard is Rs.4 Cost of 546000 sq.cm of cardboard is ? 

= Rs. 2184