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

Answer 1

Answer:

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For Bigger Cardboard box:

Given :

• Length (l) = 25cm
• Breadth (b) = 20cm
• Height (h) = 5cm

Total Surface Area of Bigger Cardboard :

★ 2(lb+bh+hl) ★

=> 2 (25×20 + 20×5 + 5×25)

=> 2 ( 500 + 100 + 125 )

=> 2 ( 725 )

=> 1450cm²

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

=> 5% of 1450

=> 5/100 × 1450 = 72.5cm²

Total surface area of Bigger Cardboard with extra overlaps:

=> 1450 + 72.5

=> 1522.5cm²

Then, Total Surface Area with extra overlaps of 250 such boxes:

=> 250 × 1522.5

=> 380625cm²

Since, Cost of Cardboard for 1000cm² is Rs.4

Cost of Cardboard for 1cm² = Rs. 4/1000

Cost of Cardboard for 380625cm² :-

=> Rs. 4/1000 × 380625

=> Rs. 1522.50

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For Smaller Cardboard box:

Given :

• Length (l) = 15cm
• Breadth (b) = 12cm
• Height (h) = 5cm

Total Surface Area of Smaller Cardboard :

★ 2(lb+bh+hl) ★

=> 2 ( 15×12 + 12×5 + 5×15 )

=> 2 ( 180 + 60 + 75 )

=> 2 ( 315 )

=> 630cm²

5% of extra surface of total surface area is required for all the overlaps:

=> 5% of 630

=> 5/100 × 630 = 31.5cm²

Total Surface Area with extra overlaps:

=> 630 + 31.5

=> 661.5cm²

Then, Total Surface Area with extra overlaps of 250 such smaller boxes:

=> 250 × 661.5

=> 165375cm²

Since, Cost of Cardboard for 1000cm² is Rs.4

Cost of Cardboard for 1cm² = Rs. 4/1000

Cost of Cardboard for 165375cm² :-

=> Rs. 4/1000 × 165375

=> Rs. 661.50

_____________________

Therefore, Total Cost of the Cardboard required for supplying 250 boxes of each kind:

★ Total Cost of bigger boxes + Total Cost of smaller boxes ★

=> Rs. 1522.50 + Rs. 661.50

=> Rs. 2184

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★ More Information ★

CSA = Curved Surface Area

TSA = Total Surface Area

★ CSA of Cylinder = 2πrh

★ TSA of Cylinder = 2πr(r+h)

★ Volume of Cylinder = πr²h

★ CSA of Cone = πrl

★ TSA of Cone = πr(l+r)

★ Volume of Cube = (side)³

★ CSA of Cube = 4(side)²

★ TSA of Cube = 6(side)²

★ Volume of Cuboid = lbh

★ CSA of Cuboid = 2(l+b)h

★ TSA of Cuboid =2(lb+bh+hl)

Answer 2

$\fbox \red{ANSWER : }$

☯️Dimensions of bigger box:

l=25 cm

b=20 cm

h =5 cm

☯️surface area of the box:

=2(25×20+25×5+20×5) cm²

=2(500+125+100)

=1450 cm²

Additional area required for overlapping:

$\frac{1450 \times 5}{100} {cm}^{2} =72.5 \mathrm{cm}^{2}$

∴ Total surface area:

$=1450+72.5=1522.5 {cm}^{2}$

So,Area of cardboard sheet for 250 such boxes

=(1522.5×250) cm ²

=380625

☯️Dimensions of small box:

l=15 cm

b=12 cm

h = 5 cm

☯️total Surface area:

=2(15×12+15×5+12×5)cm² =630 cm²

✴️For overlapping area 630×5/100=31.5²

☯️Total surface area:

=630+31.5=661.5 cm²

✴️Area of cardboard sheet required for 250 boxes of each kind:

=250×661.5cm²

=165375 cm²

☯️the total surface area required = (380625+ 165375)cm²=546000cm²

✴️Cost of cardboard for 1000cm²= Rs.4

∴546000×4/1000=Rs.2184

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