A solid irregular object has a mass of 78.4 g. When submerged in a graduated cylinder, it raises the water level from 20 mL to 50 mL. What is the density of the object?

The volume of the irregular solid is determined by the displacement of water.
Given initial water level = $20\, \text{mL}$ and final water level = $50\, \text{mL}$.

$$\text{Volume of solid} = \text{Final water level} - \text{Initial water level}$$ $$\text{Volume of solid} = 50\, \text{mL} - 20\, \text{mL}$$ $$\text{Volume of solid} = 30\, \text{mL}$$

The density is given by the formula $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$.
Given mass of solid = $78.4\, \text{g}$ and calculated volume of solid = $30\, \text{mL}$.

$$\text{Density} = \frac{78.4\, \text{g}}{30\, \text{mL}}$$ $$\text{Density} = 2.6133...\,\text{g/mL}$$ $$\text{Density} \approx 2.61\, \text{g/mL}$$

The density of the irregular solid is $\text{2.61 g/mL}$.