Question

Copper can be drawn into thin wires. How many meters of 34−gauge wire

(diameter = 6.304 ×10⁻³ in)

can be produced from the copper in 7.20 lb of covellite, an ore of copper that is 66.0% copper by mass?

(Hint: Treat the wire as a cylinder: V of cylinder = πr²h; d of copper = 8.95 g/cm³).

Answer 1

Sol:-

data provided in the question is :-

• mass of covellite = 7.20 lb
• core in ore is 66.0% = 0.66
• density of copper = 8.95 g/ cm³
• volume of cylinder = 2πrh

To be find number of wire of following property :-

• length of wire = 34-guage wire = 0.16 mm = 0.016 cm
• diameter = 6.304 * 10^-3 in.
• radius (r) = 3.152 * 10^-3 in. = 3.152* 10^-3 *2.54 cm​​​​​​​

=8.006 * 10^-3 cm

and,

) 1 lb = 0.45 kg

) 34-guage = 0.16 mm

) 1 mm = 0.001 m

) 1 cm = 10 mm

) 1 in. = 2.54 cm

) π = 3.14

) 1 Kg = 1000 g

calculation,

) mass of covellite in kg = (7.20 * 0.45 )kg

= 3.24 kg

) mass of copper in ore =( 3.24 * 0.66 ) kg

= 2.1384 kg

= (2.1384 * 1000 ) g

= 2138.4 g

from question -

) Volume of wire of length 0.16 mm = volume of cylinder of lenght 0.16 mm

volume of cylinder =( 2 * π * r * h)

= (2 * 3.14 * 8.006 * 10^-3 * 0.016 ) cm³

= (0.80444 * 10^-3) cm³

mass of copper cylinderical wire = (density) * ( volume of wire)

= (8.95 * 0.80444 * 10^-3) g

= ( 7.1997 * 10^-3) g

mass of the copper wire = (7.1997 * 10^-3) g

Let the number of wire is "n" ,

n * ( mass of wire) = mass of copper

n * ( 7.1997 * 10^-3) g = 2138.4 g

n = 2138.4 / ( 7.1997 * 10^-3)

= (2138.4 / 7.1997 ) * 10³

= 297.01 * 10³

297000

number of wire "" n "" = 297000   Answer