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

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29 Aug 2019, 23:37
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65% (hard)

Question Stats:

52% (02:02) correct 48% (02:34) wrong based on 29 sessions

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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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Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm  [#permalink]

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30 Aug 2019, 01:39
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Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm  [#permalink]

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30 Aug 2019, 02:33
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8mm is the primeter of the wire.
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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Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm  [#permalink]

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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.

A. $16π/10000 _________________ On the way to conquer the GMAT and I will not leave it until I win. WHATEVER IT TAKES. Target 720+ " I CAN AND I WILL" Your suggestions will be appreciated here---> https://gmatclub.com/forum/your-one-advice-could-help-me-poor-gmat-scores-299072.html 1) Gmat prep: [620 Q48 V27], 2) Gmat prep: [610 Q47 V28], 3) Gmat prep: [620 Q47 V28], 4) Gmat prep: [660 Q47 V34], 5) Gmat prep: [560 Q37 V29], 6) Gmat prep: [540 Q39 V26], 7) Veritas Cat: [620 Q46 V30], 8) Veritas Cat: [630 Q45 V32], 9) Manhattan:[630 Q41, V35] Senior Manager Joined: 07 Mar 2019 Posts: 311 Location: India GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities) Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm [#permalink] ### Show Tags 30 Aug 2019, 06:52 1 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). _________________ Ephemeral Epiphany..! GMATPREP1 590(Q48,V23) March 6, 2019 GMATPREP2 610(Q44,V29) June 10, 2019 GMATPREPSoft1 680(Q48,V35) June 26, 2019 GMAT Club Legend Joined: 18 Aug 2017 Posts: 4976 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm [#permalink] ### Show Tags 30 Aug 2019, 09:31 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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Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm  [#permalink]

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30 Aug 2019, 09:52

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).
Re: A square of area 16m^2 is made from a metal wire of a thickness of 8mm   [#permalink] 30 Aug 2019, 09:52
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