In 1983, the United States began coining the cent piece out...

In $1983,$ the United States began coining the cent piece out of copper-clad rinc rather than pure copper. The mass of the old copper penny is $3.083 \mathrm{g},$ while that of the new cent is 2.517 g. Calculate the percentage of sinc (by volume) in the new cent. The density of copper is $8.960 \mathrm{g} / \mathrm{cm}^{3}$ and that of zinc is $7.133 \mathrm{g} / \mathrm{cm}^{3} .$ The new and old coins have the same volume.

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00:01 All right, so we have a penny that was originally made of only copper and had a mass of, let's see, what was it, 3 .083 grams.

00:14 And now we have a newly minted penny that is a combination of copper and zinc, and it has a mass of 2 .517 grams, i believe.

00:26 And so, or, yeah, 517.

00:28 And so we want to know how much of the new penny is made as a percentage of its total volume compared to the previous one, which is 0 % zinc.

00:38 So first off, let's find the volume of the penny.

00:40 We're told the volumes are the same.

00:42 So the volume is going to be the mass divided by the density.

00:46 And so this would be 3 .083 grams for the copper penny divided by 8 .96 grams per cubic centimeter.

00:55 And so this is 0 .344.

00:58 Cubic centimeters.

01:00 So that's the volume of the new penny as well.

01:03 And one thing we'll need later for this new penny is let's compute the density really quickly.

01:07 So 2 .517 grams over 0 .344 grams per cubic centimeters.

01:19 This gives us a density of about 7 .316 grams per cubic centimeter.

01:24 So that's for the new penny.

01:26 Now what we have is that the mass of the new penny is going to be the density of copper times the volume of copper in the penny, right? because that's basically how much copper there is...

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