Question

Please, give me the answer:

The question is from class IX , board SEBA for Assam.

Question: Ex-13.1,question no 7

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 × 12cm × 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.
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Answer 1

Given :

• Dimensions of Big Box = 25cm × 20cm × 5cm.
• Dimensions of Small Box = 15cm × 12cm × 5cm.

To Find :

• Cost of Cardboard required for supplying 250 boxes of each kind.

Solution :

For Big Box :

• Length = 25cm
• Breadth = 20cm
• Height = 5cm

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Big\:Box=2(lb+bh+hl)}$

Putting Values :

$\longmapsto\tt{2(25\times{20}+20\times{5}+5\times{25)}}$

$\longmapsto\tt{2(500+100+125)}$

$\longmapsto\tt{2(725)}$

$\longmapsto\tt\bf{1450{cm}^{2}}$

Extra Area of 5 % :

$\longmapsto\tt{145{\cancel{0}}\times\dfrac{5}{10{\cancel{0}}}}$

$\longmapsto\tt{145\times\dfrac{5}{10}}$

$\longmapsto\tt{\dfrac{725}{10}}$

$\longmapsto\tt\bf{72.5{cm}^{2}}$

Total Area of Big Box :

$\longmapsto\tt{1450+72.5}$

$\longmapsto\tt\bf{1522.5{cm}^{2}}$

Area of 250 boxes :

$\longmapsto\tt{25{\cancel{0}}\times\dfrac{15225}{1{\cancel{0}}}}$

$\longmapsto\tt{25\times{15225}}$

$\longmapsto\tt\bf{380625{cm}^{2}}$

So , The Area of 250 boxes is 380625cm..

For Small Box :

• Length = 15cm
• Breadth = 12cm
• Height = 5cm

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Small\:Box=2(lb+bh+hl)}$

Putting Values :

$\longmapsto\tt{2(15\times{12}+12\times{5}+5\times{15)}}$

$\longmapsto\tt{2(180+60+75)}$

$\longmapsto\tt{2(315)}$

$\longmapsto\tt\bf{630{cm}^{2}}$

Extra Area of 5 % :

$\longmapsto\tt{630\times\dfrac{5}{100}}$

$\longmapsto\tt\bf{31.5{cm}^{2}}$

Total Area of Small Box :

$\longmapsto\tt{630+31.5}$

$\longmapsto\tt\bf{661.5{cm}^{2}}$

Area of 250 boxes :

$\longmapsto\tt{25{\cancel{0}}\times{6615}{1{\cancel{0}}}}$

$\longmapsto\tt{25\times{6615}}$

$\longmapsto\tt\bf{165375{cm}^{2}}$

Now ,

$\longmapsto\tt{Area\:of\:both\:boxes=380625+165375}$

$\longmapsto\tt\bf{546000{cm}^{2}}$

Cost of 1000cm² Cardboard = ₹4

$\longmapsto\tt{Cost\:of\:1{cm}^{2}\:Cardboard=\dfrac{4}{1000}}$

$\longmapsto\tt{546{\cancel{000}}\times\dfrac{4}{{\cancel{1000}}}}$

$\longmapsto\tt{564\times{4}}$

$\longmapsto\tt\bf{Rs.2184}$

So , The Cost of Cardboard of both boxes is Rs.2184..