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

25cm×20cm×5cm and the smaller of dimensions 15cm×12cm×5cm For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs.4 for 1000cm², find the cost of cardboard required for supplying 250 boxes of each kind.


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Answer 1

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Answer 2

$\large \tt \blue{ \fbox \colorbox{pink}{answer}}$

Reasoning:

• A cuboid has six faces and the total surface area is sum of the area of the six faces. So, the cost for supplying 250 boxes of each kind will be the summation of surface area of boxes multiplied by cost per cm square.

What is the known?

• Dimensions of the smaller and bigger boxes.
• Cost of the card board

What is the unknown?

• Cost of the card board required for 250

boxes of each kind.

Solution:

For bigger box:

$\tt \gray{ \: \: \: \: \: \: \: length(l) = 25cm} \\ \tt \gray{\: \: \: \: \: \: \: breadth(b) = 20cm} \\ \tt \gray{ \: \: \: \: \: \: \: height(h) = 5cm}$

Total surface area:

$\tt \red{ = 2(lb + bh + hl)} \\ \tt \red{=2[25×20+25×20+5×25]}\\ \tt \red{= 2[500+100+125 ]}\\ \tt \red{ = {1450cm}^{2} }$

Card board required for all the overlaps is 5% of their total surface area

$\tt \purple{\because \frac{5}{100} \times 630 = {31.5 \: cm}^{2} }$

Net surface area of the smaller box

$</p><p> \tt \green{=630+31.5}</p><p> \\ \tt \green{=661.5 {cm}^{2} }$

Card board required for 250 such boxes

$</p><p> \tt \orange{=661.5×250} \\ </p><p> \tt \orange{=165375 {cm}^{2} }$

Cost of the card board is Rs.4 for 1000cm2

For 165375 cm² cost is

$\tt \pink{\frac{4}{1000} \times 16537} \\ \tt \pink{= Rs.661.50 }$

Cost of card board required for supplying 250 boxes of each kind

$\tt \blue{= 1522.50 + 661.50} \\ \bf\purple{ \fbox{= Rs.2184}}$

$\large \mathfrak \red{hope \: this \: helps}$