A square of area 16m^2 is made from a metal wire of a thickness of 8mm

Question

Competition Mode Question

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

EncounterGMAT · Answer

IMO answer is option A

Here's how I did:
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Mohammadmo · Answer

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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Kinshook · Answer

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

Prasannathawait · Answer

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

unraveled · Answer

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).

Archit3110 · Answer

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

kunaldutt15 · Answer

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

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