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anonymous

  • 5 years ago

A SOLID ALUMINUM CUBE MEASUREING 15 INCHES ON A SIDE IS MELTED AND ROLLED INTO ALUMINUM WIRE THAT IS 0.2 INCHES IN DIAMETER. WHAT WILL BE THE LENGTH OF THIS WIRE?

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  1. asnaseer
    • 5 years ago
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    @HMKEFK: Call the length of the wire 'h' and then calculate its volume. Do you know how to calculate the volume of a wire given it has a circular cross-section?

  2. anonymous
    • 5 years ago
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    NOT EXACTLY

  3. asnaseer
    • 5 years ago
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    ok - the cross section of the wire is a circle. do you know how to find the area of a circle?

  4. anonymous
    • 5 years ago
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    AREA OF A CIRCLE IS 3.14RADIUS SQUARED

  5. asnaseer
    • 5 years ago
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    correct - so you are told the diameter is 0.2 inches, which means the radius must me half of this, i.e. 0.1 inches.

  6. asnaseer
    • 5 years ago
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    so the area of the circular cross section of the wire is:\[A_{crosssection}=\pi r^2=\pi(0.1)^2=\frac{\pi}{100}\]

  7. asnaseer
    • 5 years ago
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    now if we call the length of the wire 'h', then its volume is given by:\[V_{wire}=A_{crosssection}*h=\frac{\pi h}{100}\]

  8. asnaseer
    • 5 years ago
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    so you understand so far?

  9. anonymous
    • 5 years ago
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    I THINK SO!

  10. asnaseer
    • 5 years ago
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    good, so now we need to calculate the original volume of the cube. you are told that the original cube had a side length of 15 inches. so, do you know how to calculate the volume of this cube?

  11. asnaseer
    • 5 years ago
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    |dw:1326847522420:dw|

  12. anonymous
    • 5 years ago
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    NOT EXACTLY; I WAS THINKING ABOUT SURFACE AREA

  13. asnaseer
    • 5 years ago
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    no - you need to calculate its volume. the cube was melted and then reformed into a wire. so it is the volume os material that remains the same. do you know how to work out the area of one side of this cube?

  14. asnaseer
    • 5 years ago
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    |dw:1326847736701:dw|

  15. anonymous
    • 5 years ago
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    NO

  16. asnaseer
    • 5 years ago
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    each side face of a cube is a square. the area of one side face is therefore equal to the area of a square of side length 15 inches. do you know how to calculate that?

  17. anonymous
    • 5 years ago
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    NEGATIVE

  18. asnaseer
    • 5 years ago
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    I would recommend that you first learn these basics before tackling a problem like this. A good start might be one of these site: 1) http://www.mathsisfun.com/area.html 2) http://www.youtube.com/watch?v=YjGVFPtNTHw 3) http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7_22i2.htm

  19. asnaseer
    • 5 years ago
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    also here: http://www.youtube.com/watch?v=2vBpkgJBiZY

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