Question

1. apply concepts a 68 - g bar of gold is cut into three equal pieces. how does the density of each piece compare to the density of the original gold bar?

Explanation:

Step1: Recall density formula

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

Step2: Analyze mass - volume relationship for cut pieces

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 also $\frac{1}{3}$ of the original volume. Let the original mass be $m_1$ and 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 a piece

The density of a piece $
ho_2=\frac{m_2}{V_2}=\frac{\frac{1}{3}m_1}{\frac{1}{3}V_1}=\frac{m_1}{V_1}=
ho_1$, where $
ho_1$ is the density of the original bar.

Answer:

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