Problem

Brass is a copper–zinc alloy. What is the mass in grams of a brass cylinder having a length of 1.62 in. and a diameter of 0.514 in. if the composition of the brass is 67.0% copper and 33.0% zinc by mass? The density of copper is 8.92 g/cm3, and the density of zinc is 7.14 g/cm3. Assume that the den-sity of the brass varies linearly with composition.

Relevant Solution
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Hey everyone, we're told that in var is an iron nickel alloy and the composition of in Hvar is 64% iron with a density of 7.86 g per cubic centimeters and 36% nickel with a density of 8.90 g per cubic centimeters by mass, calculate the mass of an Inn var cylinder in grams. That is 1.95 inches in length and 0.675 inches in diameter. Assume that its density changes linearly with composition first. Let's go ahead and calculate the average density of N var. We can do so by multiplying our percentages by its respective density. So starting off with our iron, we can convert that percentage into its decimal form. So that will be 0.640. And we're going to multiply that by 7.86 g per cubic centimeters. Next we're going to add our percent nickel, converting our 36% into its decimal form. We have 0.360. And we're going to multiply that by its density of 8.90 g per cubic centimeters. This will get us to an average density of 8.2344 g per cubic centimeters. Next we want to calculate the volume of our cylinder as we've learned, the formula is going to be volume equals pi times radius squared times height 1st. Let's go ahead and get our height and we want all of our units to be consistent. So we will convert our height and our radius into centimeters. Starting with our height, we were told that we had 1.95" in length. Using our conversion factors, we know that per one inch we have 2. cm. Now when we calculate this out and cancel out our unit, we end up with a height of 4. cm. Next calculating our radius, we were told that we had 0.675 in in diameter. Since this is in diameter, we want to divide this by two in order to get our radius again. Using our conversion factor We know that 1" contains 2.54 cm. So when we calculate this out, we end up with a total of 0. cm. Now to calculate our volume, we're going to plug in our values, we have our pie and we're going to multiply this by our radius squared which is 0. cm. And we're going to square that, Multiplying this by our height of 4.953 cm. And this will get us to a volume of 11.4349 cc. Now that we have our volume. Let's go ahead and calculate our mass. To calculate our mass. We're going to take 11.4349 cubic centimeters which was our volume. And we're going to use dimensional analysis here as we calculated in our average density of in var. We know that we had 8.2344 g per one cc. So when we calculate this out, we end up with a mass of 94.2 g. And this is going to be our final answer. Now, I hope that made sense and let us know if you have any questions.