Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass. Part A If the lead

Question

Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass.
Part A
If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 3.50 cm radius?

Answer 1

 

  The volume needed for the sphere is 4/3*pi*3.5^3 = 4/3  * pi *    ( 7/2)^3

 

                                                                            = 4/3  * 22/7    *7/2 * 7/2 * 7/2

 

                                                                             = 4/3 * 11 * 7/2 * 7/2  <-- 7's cancel; 22 cancels 2

 

                                                                            = 44/3 * 49/4

 

                                                                            = 11*49/3   <--- 44 cancels 4

 

                                                                            = 539/3 = 179 and 2/3

 

The ore contains 68.5% galena. The galena contains 86.6% lead. Only 92.5% of the lead can be extracted.

Let X be the amount of ore needed.

 

92.5% of 86.6% of 68.5% of X = 539/3

 

Changing to decimals:

  .925 * .866 * .685 * X = 539/3

 

  .54871925* X = 539/3

 

 Solving for X ---->  X = 539/3 / 0.54871925 = 327.42913