Respuesta :
The volume of sphere can be calculated using the following formula:
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
Here, r is radius of the sphere which is 3.5 cm. Putting the value,
[tex]V=\frac{4}{3}\pi r^{3}=\frac{4}{3}(3.14)(3.5cm)^{3}=180 cm^{3}[/tex]
This is equal to the volume of lead, density of lead is [tex]11.34 g/cm^{3}[/tex] thus, mass of lead can be calculated as follows:
m=d×V
Putting the values,
[tex]m=11.34 g/cm^{3}\times 180 cm^{3}=2041.2 g[/tex]
Let the mass of ore be 1 g, 68.6% of galena is obtained by mass, thus, mass of galena obtained will be 0.686 g.
Now, 86.6% of lead is obtained from this gram of galena, thus, mass of lead will be:
m=0.686×0.866=0.5940 g
Therefore, 0.5940 g of lead is obtained from 1 g of ore for 100% efficiency, thus, for 92.5% efficiency
[tex]m=\frac{92.5}{100}\times 0.5940=0.54945 g[/tex]
1 g of lead obtain from[tex]\frac{1}{0.54945}=1.82[/tex] grams of ore.
Thus, 2041.2 g of lead obtain from:
[tex]2041.2\times 1.82=3.715\times 10^{3}g or 3.715 kg[/tex]
Therefore, mass of ore required to make lead sphere is 3.715 kg.
