🤓 Based on our data, we think this question is relevant for Professor Oppenheim's class at University of Colorado at Colorado Springs.

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 4**. *Calculate the mass of the brass cylinder.*

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/cm^{3}, and the density of zinc is 7.14 g/cm^{3}. Assume that the density of the brass varies linearly with composition.