1. **State the problem:** We need to find the volume of a sample of liquid mercury given its mass and density. 2. **Recall the formula for density:** Density $\rho$ is mass $m$ divided by volume $V$: $$\rho = \frac{m}{V}$$ 3. **Rearrange the formula to solve for volume:** $$V = \frac{m}{\rho}$$ 4. **Plug in the given values:** - Mass $m = 76.2$ g - Density $\rho = 13.6$ g/mL So, $$V = \frac{76.2}{13.6}$$ 5. **Calculate the volume:** $$V \approx 5.60 \text{ mL}$$ **Final answer:** The volume of the mercury sample is approximately $5.60$ mL.