Manoj sweets place an order of making 30 centimetre multiply 20 centimetre multiply 6 centimetre cardboard boxes for packing the suite for all overlaps 5% of total area is required extra if cost of cardboard is rupees 2000 centimetres square find the cost of the cardboard used for making 500 boxes
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Hi there !!
Length = l = 30 cm
Breadth = b = 20 cm
Height = h = 6 cm
Cardboard required to make 1 cuboidal box = T.S.A of the cuboid = 2(lb + bh +lh)
= 2 (30 × 20 + 20 × 6 + 30 × 6 )
= 2 × 900
= 1800 cm²
Area of overlap = 5% of T.S.A
= 5 / 100 × 1800
= 90 cm²
Total cardboard required = 1800 + 90
= 1890 cm²
Total cardboard required for 500 boxes = 1890 × 500
= 945000 cm²
Cost of cardboard for 1 cm² =Rs 2000
Total cost = 945000 × 2000
= Rs 1,89,00,00,000
Length = l = 30 cm
Breadth = b = 20 cm
Height = h = 6 cm
Cardboard required to make 1 cuboidal box = T.S.A of the cuboid = 2(lb + bh +lh)
= 2 (30 × 20 + 20 × 6 + 30 × 6 )
= 2 × 900
= 1800 cm²
Area of overlap = 5% of T.S.A
= 5 / 100 × 1800
= 90 cm²
Total cardboard required = 1800 + 90
= 1890 cm²
Total cardboard required for 500 boxes = 1890 × 500
= 945000 cm²
Cost of cardboard for 1 cm² =Rs 2000
Total cost = 945000 × 2000
= Rs 1,89,00,00,000
Answered by
4
Solution;-
There is a mistake in this question. The cost of the cardboard must be Rs. 2 per 1000 sq cm instead of Rs. 2000 per sq cm because the shopkeeper will suffer huge loss in the second case (i.e. cost of cardboard is Rs. 2000 per sq cm. The cost of 500 boxes is 1890000000, so the cost of 1 box will be Rs. 3780000. How can it be possible ?). But, I have solved this question according to both the costs.
Length of each cardboard box = 30 cm
Breadth of each cardboard box = 20 cm
Height of each cardboard box = 6 cm
Total surface area of each cardboard box = 2(L*B + B*H + H*L)
⇒ 2(30*20 + 20*6 + 6*30)
⇒ 2(600 + 120 + 180)
⇒ 2*900
⇒ 1800 sq cm
Area of each cardboard box is 1800 sq cm
Cardboard required for 1 box = 105 % of 1800
⇒ (105*1800)/100
⇒ = 1890 sq cm
Cardboard required for 500 boxes = (1890*500) sq cm
If the cost of cardboard is Rs. 2000 per sq m, then
Total cost of making 500 boxes = 1890*500*2000
⇒ Rs. 1890000000
If the cost of cardboard is Rs. 2 per 1000 sq cm, then
Total cost of making 500 boxes = (1890*500*2)/1000
⇒ 1890000/1000
⇒ Rs. 1890
The cost of the cardboard mentioned in the question is literally impossible.
There is a mistake in this question. The cost of the cardboard must be Rs. 2 per 1000 sq cm instead of Rs. 2000 per sq cm because the shopkeeper will suffer huge loss in the second case (i.e. cost of cardboard is Rs. 2000 per sq cm. The cost of 500 boxes is 1890000000, so the cost of 1 box will be Rs. 3780000. How can it be possible ?). But, I have solved this question according to both the costs.
Length of each cardboard box = 30 cm
Breadth of each cardboard box = 20 cm
Height of each cardboard box = 6 cm
Total surface area of each cardboard box = 2(L*B + B*H + H*L)
⇒ 2(30*20 + 20*6 + 6*30)
⇒ 2(600 + 120 + 180)
⇒ 2*900
⇒ 1800 sq cm
Area of each cardboard box is 1800 sq cm
Cardboard required for 1 box = 105 % of 1800
⇒ (105*1800)/100
⇒ = 1890 sq cm
Cardboard required for 500 boxes = (1890*500) sq cm
If the cost of cardboard is Rs. 2000 per sq m, then
Total cost of making 500 boxes = 1890*500*2000
⇒ Rs. 1890000000
If the cost of cardboard is Rs. 2 per 1000 sq cm, then
Total cost of making 500 boxes = (1890*500*2)/1000
⇒ 1890000/1000
⇒ Rs. 1890
The cost of the cardboard mentioned in the question is literally impossible.
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