Question

Malachite is a mineral that contains 57.7% of copper. How many meter of wire with diameter of 0.0179 in can be produced from 6.48 lb of malachite?
V_cylinder = π*r²h, density of copper is 8.96 g/cm³, 1 lb=454 g

190 m

7.54 × 10⁵ m

2.97 × 10³ m

1.17 × 10³ m

292 m

Answer 1

given

mass of malachite = 6.48 lb

% of copper in malachite = 57.7% of copper

wire diameter = 0.0179 inch ==> radius = 0.0179/2 inch = 8.95 * 10^-3 inch

density of copper = 8.96 g/cm³

1 lb=454 g

6.48 lb = 6.48 lb * 454 g /  1 lb = 2941.92 g

mass of copper = 2941.92 g * 57.7%

= 2941.92 g * 57.7/100

= 1697.488 g Copper

density = mass / volume

volume = mass / density

=  1697.488 g / 8.96 g/cm³

= 189.45 cm³

but

Volume(V) = π*r²h

r = 8.95 * 10^-3 inch

1 inch = 0.0254 m

8.95 * 10^-3 inch = 8.95 * 10^-3 inch * 0.0254 m / inch = 2.27 * 10^-4 m

so

V = π * (2.27 * 10^-4 m)² * h

1 cm = 10^-2 m

1 cm³ = 10^-6 m³

189.45 cm³ = 189.45 cm³ * 10^-6 m³ /  cm³ = 189.45 * 10^-6 m³

189.45 * 10^-6 m³ = π * (2.27 * 10^-4 m)² * h

h =   189.45 * 10^-6 m³ /  π * (2.27 * 10^-4 m)²

h = 1170 m

= 1.17 * 10³ m