Question

1. how would the density of a solid uniform material change if you cut it into thirds?

Explanation:

Step1: Recall density formula

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

Step2: Analyze mass - volume relationship when cutting

When a solid uniform material is cut into thirds, the mass of each part $m_{new}$ is one - third of the original mass $m$ (i.e., $m_{new}=\frac{1}{3}m$), and the volume of each part $V_{new}$ is one - third of the original volume $V$ (i.e., $V_{new}=\frac{1}{3}V$).

Step3: Calculate new density

Substitute into the density formula for the new part: $
ho_{new}=\frac{m_{new}}{V_{new}}=\frac{\frac{1}{3}m}{\frac{1}{3}V}$. The $\frac{1}{3}$ terms cancel out, and $
ho_{new}=\frac{m}{V}=
ho$.

Answer:

The density would not change.