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Mathematics
OpenStudy (anonymous):

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?

OpenStudy (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?

OpenStudy (anonymous):

NOT EXACTLY

OpenStudy (asnaseer):

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

OpenStudy (anonymous):

AREA OF A CIRCLE IS 3.14RADIUS SQUARED

OpenStudy (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.

OpenStudy (asnaseer):

so the area of the circular cross section of the wire is:\[A_{crosssection}=\pi r^2=\pi(0.1)^2=\frac{\pi}{100}\]

OpenStudy (asnaseer):

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

OpenStudy (asnaseer):

so you understand so far?

OpenStudy (anonymous):

I THINK SO!

OpenStudy (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?

OpenStudy (asnaseer):

|dw:1326847522420:dw|

OpenStudy (anonymous):

NOT EXACTLY; I WAS THINKING ABOUT SURFACE AREA

OpenStudy (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?

OpenStudy (asnaseer):

|dw:1326847736701:dw|

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