33. apply concepts a 68 - g bar of gold is cut into three equal pieces. how does the density of each piece…

Explanation:

Step1: Recall density formula

Density $\rho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Analyze mass - volume change

When the gold bar is cut into three equal pieces, the mass $m$ of each piece is $\frac{1}{3}$ of the original mass, and the volume $V$ of each piece is $\frac{1}{3}$ of the original volume. Let the original mass be $m_1$ and original volume be $V_1$, and for a piece, mass be $m_2$ and volume be $V_2$. So $m_2 = \frac{1}{3}m_1$ and $V_2=\frac{1}{3}V_1$.

Step3: Calculate density of piece

The density of the original bar $\rho_1=\frac{m_1}{V_1}$, and the density of a piece $\rho_2=\frac{m_2}{V_2}=\frac{\frac{1}{3}m_1}{\frac{1}{3}V_1}=\frac{m_1}{V_1}$.

Answer:

The density of each piece is the same as the density of the original gold bar.