# 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. If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 3.00 cm radius?

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. If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 3.00 cm radius?

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Step 1

The volume needed for the sphere is = 4/3*π*(r)3

= 4/3*π*(3.0)3

= 4/3  * π * ( 27)

= 4/3  * 22/7    * (27)

= 119.26 cm3

Step 2

The ore consists of 68.5% galena while galena consists 86.6% lead.

Only 92.5% of the lead can be extracted.

Assuming X as the amount of ore needed.

Step 3

The mass of ore can be determined as:

92.5% of 86.6% of 68.5% of X = 119.26

0.925 * 0.866 * 0....

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