## 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?

1. asnaseer

@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

NOT EXACTLY

3. asnaseer

ok - the cross section of the wire is a circle. do you know how to find the area of a circle?

4. anonymous

AREA OF A CIRCLE IS 3.14RADIUS SQUARED

5. asnaseer

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

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

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

so you understand so far?

9. anonymous

I THINK SO!

10. asnaseer

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

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12. anonymous

NOT EXACTLY; I WAS THINKING ABOUT SURFACE AREA

13. asnaseer

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

|dw:1326847736701:dw|

15. anonymous

NO

16. asnaseer

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

NEGATIVE

18. asnaseer

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