Dioptase is a mineral that contains 45.3% of copper. How many
meter of wire with diameter of 0.0571 in can be produced from 3.54
lb of dioptase?
V_{cylinder} = π*r^{2}h, density of copper is 8.96
g/cm^{3}, 1 lb=454 g
3.54 Ib = 454*3.54
= 1607.16 grams
mass of copper = 45.3 % of dioptase
= 45.3 * 1607.16 /100
= 728.04 grams
suppose length of wire = l
diameter = 0.0571 in = 0.145 cm
r = d/2
= 0.145 / 2
= 0.0725 cm
volume of copper wire = 22/7 * r^2 * l
mass of wire = volume * density
= 22/7 * r^2 * l * 8.96
this is equal to 728.04 grams
22/7 * (0.0725)^2 * l * 8.96 = 728.04
l = 4918.657 cm
or 49.19 m
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