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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 29 Aug 2019, 23:37
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A
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm. What is the approximate total cost of the metal used? (Cost of metal is $6.25 per m^3)


A. $\(\frac{16 \pi}{10000}\)

B. $\(\frac{8\pi}{1000}\)

C. $\(\frac{16\pi}{1000}\)

D. $\(\frac{16\pi}{100}\)

E. $\(16\pi\)
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A
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 01:39
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IMO answer is option A

Here's how I did:
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 02:33
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8mm is the primeter of the wire.
So, 4mm is it's radius.
4mm=4*10^-3m
Pi*r^2=pi*(4×10^-3)^2
The length of the wire is 4×4=16m
So, 16 ×pi(4×10^-3)^2 ×6.25$=
16pi/10000$
Option A

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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 04:36
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Given: A square of area 16m^2 is made from a metal wire of a thickness of 8mm.

Asked: What is the approximate total cost of the metal used? (Cost of metal is $6.25 per m^3)

A square of area 16m^2 is made from a metal wire of a thickness of 8mm.
Side of the square = 4 m
Perimeter of the square = 16 m = Length of the metal wire
Thickness of metal wire = 8 mm = \(8 * 10^{-3} m =\) Diameter of cross-section
Area of metal wire cross-section = \(\pi * (4 * 10^{-3})^2 m^2\)

Volume of metal wire used = Area of cross-section * length of wire = \(\pi * (4 * 10^{-3})^2 * 16 m^3\)
Cost of the metal wire = \($6.25 * \pi * 16 * 10^{-6} * 16 = 16 \pi * 100 * 10^{-6} = $16\pi /10000\)

IMO A
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 04:57
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IMO A is the right answer.
We have to use a formula for the cylinder. So it's πr^2h. Here r = 4/1000meters, and h = 16 meters.
So, the cost of metal would be 6.25 * π * (4/1000)^2 * 16 = 16π/10000

A square of area 16m^2 is made from a metal wire of a thickness of 8mm. What is the approximate total cost of the metal used? (Cost of metal is $6.25 per m^3)

A. $16π/10000
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 06:52
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Since metal wire has a thickness of 8 mm the radius of wire equates to 4 mm. Side of square of area \(16m^2\) formed using wire equals 4m. Given cost of wire = \(6.25 m^3\).

Thus total length of wire, \(l = 4 * 4 m\)

Hence volume of metal \(= π * r^2 * l\)

Total cost of wire, \($ = π * r^2 * l * 6.25\)
 Cost, \($ = π * 4 * 4 * \frac{1}{10}^3 * \frac{1}{10}^3 * 16 * 6.25\)
 Cost, \($ = π * 16 * 16 * 625 * \frac{1}{10}^8\)

Looking into the answer choices keep 16 and π in the calculations.

Thus Cost, \($ = π * 16 * 10^4 * \frac{1}{10}^8\)
 Cost, \($ = π * 16 * \frac{1}{10}^4\)

Hence, Answer (A).
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 09:31
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thickness ; 8mm ; 0.008 m
area ; 16m^2 ; radius ; 4

pi * r^2*h * 6.25 ; $16π/10000
IMO A

A square of area 16m^2 is made from a metal wire of a thickness of 8mm. What is the approximate total cost of the metal used? (Cost of metal is $6.25 per m^3)


A. $16π/10000
B. $8π/1000

C. $16π/1000

D. $16π/100

E. $16π
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 30 Aug 2019, 09:52
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Answer is A.

Area of the square= \(16 m^2\)
=> side length of square= \(4m\)
=> perimeter of the square = \(16m\) = length of the wire used (or height)

Thickness of the wire = diameter = \(8mm\)
=> radius = \(4mm\) = \(4/1000m\)

Volume of the wire = \(π*r^2*h\) = \(π * (4/1000)^2* 16\)

Cost = $ \(6.25 * volume\)

= \(625/100 * π * 4/1000 * 4/1000 * 16\)
=\(16π/10000\) (Option A).
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A square of area 16m^2 is made from a metal wire of a thickness of 8mm 15 Jul 2023, 04:43
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