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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Density concept. You can view video lessons to learn Density. Or if you need more Density practice, you can also practice Density practice problems.

What professor is this problem relevant for?

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