a copper wire ( density = 8.96 g/cm^3 ) has a diameter of 0.25 mm. if a sample of this copper wire has a mass of 22 g, how long is the wire?

V = πr²H
r = 0,25mm / 2 = 0,125mm = 0,0125cm
d = 8,96 g/cm³
m = 22g

[tex]d=\frac{m}{V}\\\\ \pi r^{2}H=\frac{m}{d}\\\\ H=\frac{m}{\pi r^{2}d}=\frac{22g}{\pi *(0,0125cm)^{2}*8,96\frac{g}{cm^{3}}}=\frac{22g}{3,14*0,00015625cm^{2}8,96\frac{g}{cm^{3}}}=\\\\\\\approx5004,55cm=50,0455m[/tex]

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Muscardinus Muscardinus · Answer 2 · 2019-08-29T09:34:53+02:00

Answer:

The length of the copper wire is 50.02 meters.

Explanation:

It is given that,

Density of the copper wire, [tex]d=8.96\ g/cm^3=8960\ kg/m^3[/tex]

Diameter of copper wire, d = 0.25 mm = 0.00025 m

Radius of the copper wire, r = 0.000125 m

Mass of the copper, m = 22 g = 0.022 kg

We need to find the length of the wire. Let l is the length of the wire. The density of a copper wire is given by :

[tex]d=\dfrac{m}{V}[/tex]

V is the volume of copper wire

[tex]d=\dfrac{m}{\pi r^2h}[/tex]

[tex]h=\dfrac{m}{d\pi r^2}[/tex]

[tex]h=\dfrac{0.022\ kg}{8960\ kg/m^3\times \pi (0.000125\ m)^2}[/tex]

h = 50.02 m

So, the length of the wire is 50.02 meters. Hence, this is the required solution.