I am confused on the wording of this question and what procedure it wants me to follow. so if anyone could help me that would be great:Copper has a density of 8.94g/cm^3. If a factory has a bar of solid copper that has a mass of 57.0kg and it is drawn into a wire with a diameter of 9.50mm, what length of a wire, in meters, can be produced?Conversion factors that may help (that I know of):1m 10^3mm1m^3 10^6cm^3Please any help is appreciated and please show your thought process if you do the problem out. Thanks in advance!
The wire is just a long cylinder. The volume of a cylinder is cross sectional area x length. The total volume of copper in the bar is the mass divided by the density. The equation is: volume length x cross sectional area Calculate volume and area then solve for length.
If the wire has a diameter od 9.50mm you need to first workout the surface area which is. pi x radius squared 3.1416 x (9.50 / 2) x (9.50 / 2) 70.88 mm2 0.7088 cm2 Then you need to work out the volume of copper that you have which is. mass / density (57 x 1000) / 8.94 6375.8 cm3 Finally workout the length which is. volume / surface area 6375.8 / 0.7088 8995cm (possibly 9000 if rounded more accurately) 89.98 m (possibly 90m).
This is quite simple, actually. First, convert the mass to volume by means of the density, then assume the wire has a cylindrical shape and work back from there. Volume mass/density, so 57,000/8.94 6375.84 cm? of copper Volume of cylinder πr?h We have the volume and the radius, so find h. 6375.84 π(4.75)?h, so h 6375.84 cm?/π×22.5625 cm? 89.95 cm, correct to 2 decimal places.
