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 ×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
Answers & Comments
Answer:
[tex]\boxed{\bf\:Cost \: of \: cardboard\:required \: for \: 250 \: boxes \: is \: Rs \: 2184 \: } \\ [/tex]
Step-by-step explanation:
Dimensions of bigger box
Length of bigger box, l = 25 cm
Breadth of bigger box, b = 20 cm
Height of bigger box, h = 5 cm
So,
[tex]\sf\: Cardboard\:required \: for \: 1 \: bigger \: box \\ [/tex]
[tex]\sf\: = \: TSA_{(Cuboid)} \\ [/tex]
[tex]\sf\: = \: 2(lb + bh + hl) \\ [/tex]
[tex]\sf\: = \: 2(25 \times 20 + 20 \times 5 + 5 \times 25) \\ [/tex]
[tex]\sf\: = \: 2(500 + 100 + 125) \\ [/tex]
[tex]\sf\: = \: 2 \times 725 \\ [/tex]
[tex]\sf\: = \: 1450 \\ [/tex]
Thus,
[tex]\sf\: Cardboard\:required \: for \: 1 \: bigger \: box = 1450 \: {cm}^{2} \\ [/tex]
Now,
[tex]\sf\: Extra\:cardboard\:required = 5\% \: of \: TSA_{(bigger \: box)} \\ [/tex]
[tex]\sf\: Extra\:cardboard\:required = \dfrac{5}{100} \times 1450 = 72.5 \: {cm}^{2} \\ [/tex]
Thus,
[tex]\sf\: Amount \: of \: cardboard\:required \: for \: 1 \: bigger \: box = 1450 + 72.5 = 1522.5 \: {cm}^{2} \\ [/tex]
Now,
[tex]\sf\: Amount \: of \: cardboard\:required \: for \: 250 \: bigger \: box \\ [/tex]
[tex]\sf\: = \: 250 \times 1522.5 \\ [/tex]
[tex]\sf\: = \: 380625 \: {cm}^{2} \\ [/tex]
Dimensions of smaller box
Length of smaller box, l = 15 cm
Breadth of smaller box, b = 12 cm
Height of smaller box, h = 5 cm
So,
[tex]\sf\: Cardboard\:required \: for \: 1 \: smaller \: box \\ [/tex]
[tex]\sf\: = \: TSA_{(Cuboid)} \\ [/tex]
[tex]\sf\: = \: 2(lb + bh + hl) \\ [/tex]
[tex]\sf\: = \: 2(15 \times 12 + 12 \times 5 + 5 \times 15) \\ [/tex]
[tex]\sf\: = \: 2(180 + 60 + 75) \\ [/tex]
[tex]\sf\: = \: 2 \times 315 \\ [/tex]
[tex]\sf\: = \: 630 \: {cm}^{2} \\ [/tex]
Thus,
[tex]\sf\: Cardboard\:required \: for \: 1 \: smaller \: box = 630 \: {cm}^{2} \\ [/tex]
Now,
[tex]\sf\: Extra\:cardboard\:required = \dfrac{5}{100} \times 630 = 31.5 \: {cm}^{2} \\ [/tex]
So,
[tex]\sf\: Amount \: of \: cardboard\:required \: for \: 1 \: smaller \: box = 630 + 31.5 = 661.5 \: {cm}^{2} \\ [/tex]
Now,
[tex]\sf\: Amount \: of \: cardboard\:required \: for \: 250 \: smaller \: box \\ [/tex]
[tex]\sf\: = \: 250 \times 661.5 \\ [/tex]
[tex]\sf\: = \: 165375 \: {cm}^{2} \\ [/tex]
Thus,
[tex]\bf\: Total \: cardboard\:required \: for \: 250 \: boxes \: of \: each \: type \\ [/tex]
[tex]\sf\: = \: 380625 + 165375 \\ [/tex]
[tex]\sf\: = \: 546000 \: {cm}^{2} \\ [/tex]
So,
[tex]\implies\bf\: Total \: cardboard\:required = 546000 \: {cm}^{2} \\ [/tex]
Now, Further given that the cost of the cardboard is Rs 4 for 1000 cm².
So,
[tex]\sf\: Cost \: of \: cardboard\:required = 564000 \times \dfrac{4}{1000} \\ [/tex]
[tex]\implies\sf\: Cost \: of \: cardboard\:required = Rs \: 2184 \\ [/tex]
Hence,
[tex]\implies \boxed{\bf\:Cost \: of \: cardboard\:required \: for \: 250 \: boxes \: is \: Rs \: 2184 \: } \\ [/tex]