1. The problem asks for the density of a substance given the mass and volume. 2. Density ($\rho$) is defined as mass divided by volume: $$\rho = \frac{m}{V}$$ 3. Given mass $m = 84.7$ grams and volume $V = 49.6$ cm$^3$. 4. Substitute the values into the density formula: $$\rho = \frac{84.7}{49.6}$$ 5. Calculate the density: $$\rho \approx 1.708$ g/cm$^3$$ 6. Therefore, the density of the substance is approximately $1.71$ g/cm$^3$.