# Problem: Brass is a copper-zinc alloy.What is the mass in grams of a brass cylinder having a length of 2.02 in. and a diameter of 0.492 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 density of the brass varies linearly with composition.

###### FREE Expert Solution

In this problem, we are asked to determine the mass of the brass cylinder having a length of 2.02 in. and a diameter of 0.492 in.

Recall that density is the ratio of the mass and volume of an object:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume of a sphere is given by:

$\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{4}}{\mathbf{3}}{{\mathbf{\pi r}}}^{{\mathbf{2}}}{\mathbf{h}}}$

where:

h = height or length; r = radius. Recall that diameter = 2r.

To solve this problem, we need to do the following:

Step 1. Determine the volume of the cylinder.
Step 2. Determine the volume of copper and zinc present.
Step 3. Determine the mass of Cu and Zn.
Step 4Calculate the mass of the brass cylinder.

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###### Problem Details

Brass is a copper-zinc alloy.

What is the mass in grams of a brass cylinder having a length of 2.02 in. and a diameter of 0.492 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 density of the brass varies linearly with composition.