Question

A box contains a mixture of cobalt spheres and palladium spheres. The total mass of the combined spheres is 3.98 kg, and the total volume of both metals is 411 mL. What percentage of the spheres are cobalt?

Answer 1

volume = 411 ml = 411 cm^3

mass = 3.98 kg = 3980 g

density of cobalt = 8.86 g/cm^3
density of palladium = 11.90 g/cm^3
Now,
density = mass / volume
mass = density x volume


Let volume of cobalt = A
mass of cobalt = density x volume

= 8.86 g/cm^3 x A
= 8.86A

Let Volume of palladium = B
mass of palladium = density x volume

= 11.90 g/cm^3 x B
= 11.90B
Total mass of the two spheres = 3980 g
3980 g = mass of cobalt + mass of palladium
3980 =  8.86A + 11.90B

Now,
Total volume = A + B = 411 cm^3
B = 411 - A
Now,
3980 = 8.86A + 11.90 B
3980 = 8.86A + 11.90 (411 - A)
3980 = 8.86 A + 4890.9 - 11.90A
A = 299.64

Volume of Cobalt = 299.64 cm^3
% of spheres of cobalt

= volume of cobalt / total volume x 100
= 299.64 cm^3 / 411 cm^3 x 100
= 72.91%