How many meters of 6.304x10^(-3)in diameter wire can be produced from for 6.70 lbs of copper ore, the ore is 66.0% copper by mass. Copper has a density of 8.95g/cm^3. Treat wire as a cylinder with v=(pi)r^(2)h. How many meter with and without significant figures.
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Mass of copper in copper ore = 66/100 x 6.70 lb = 4.422 lb
1 lb = 453.592 g, so 4.422 lb = 4.422 x 453.952 g = 2007.376 g
Volume of copper = mass/density = 2007.376 g/(8.95 g/cm^3) = 224.288 cm^3
Diameter of wire required = 6.34 x 10^-3 in
1 in = 2.54 cm, so 6.34 x 10^-3 in = 6.34 x 10^-3 x 2.54 cm = 0.0161036 cm
Radius of copper wire = Diameter/2 = 0.0161036 cm/2 = 0.0080518 cm
Volume of cylinder = 22/7 x r^2 x h
Therefore height (or length) of wire = Volume/(22/7 x r^2) = 224.288 cm^3(22/7 x 0.0080518 cm^2)
= 1100766 cm
= 11007.66 m or 11008 m
1 lb = 453.592 g, so 4.422 lb = 4.422 x 453.952 g = 2007.376 g
Volume of copper = mass/density = 2007.376 g/(8.95 g/cm^3) = 224.288 cm^3
Diameter of wire required = 6.34 x 10^-3 in
1 in = 2.54 cm, so 6.34 x 10^-3 in = 6.34 x 10^-3 x 2.54 cm = 0.0161036 cm
Radius of copper wire = Diameter/2 = 0.0161036 cm/2 = 0.0080518 cm
Volume of cylinder = 22/7 x r^2 x h
Therefore height (or length) of wire = Volume/(22/7 x r^2) = 224.288 cm^3(22/7 x 0.0080518 cm^2)
= 1100766 cm
= 11007.66 m or 11008 m