Question

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*r²h, density of copper is 8.96 g/cm³, 1 lb=454 g

Answer 1

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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