Chapter 2, Problem 1PLA

To determine

The density of the cylinder and material it is made of.

Answer to Problem 1PLA

The density of the cylinder is $8.41\text{g}/{\text{cm}}^{\text{3}}$ and material it is likely to be Brass.

Explanation of Solution

The expression to calculate the density is,

$\rho =\frac{m}{V}$

Here, $\rho$ is the density, m is the mass, and V is the volume

The expression for the volume of the cylinder is,

$V=\frac{\pi d^{2}h}{4}$

Here, d is the diameter and h is the length

Use $\frac{\pi d^{2}h}{4}$ for V in density expression and rewrite

$\begin{array}{c}\rho =\frac{m}{\frac{\pi d^{2}h}{4}}\\ =\frac{4m}{\pi d^{2}h}\end{array}$        (I)

Conclusion:

Substitute $3.23\text{cm}$ for h, $1.75\text{cm}$ for d, and $65.3\text{g}$ for $m$ in (I).

$\begin{array}{c}\rho =\frac{4\left(65.3\text{g}\right)}{\pi {\left(1.75\text{cm}\right)}^2\left(3.23\text{cm}\right)}\\ =8.41\text{g}/{\text{cm}}^{\text{3}}\end{array}$

Therefore, the density of the cylinder is $8.41\text{g}/{\text{cm}}^{\text{3}}$ and material it is likely to be Brass.