Copper has a density of $8.96 \text { gm per }cm^3$. If a cylinder of copper weighing $24.31 g$ is dropped into a graduated cylinder containing $20.00 mL$ of water, what will be the new water level?

You want to find out the volume of the copper based on its mass and density. Recall that $\textrm{mass}=\textrm{density }\cdot\textrm{ volume}$. You have an algebraic equation of this form $$ 8.96\frac{\textrm{g}}{\textrm{cm}^3}\cdot x\textrm{ cm}^3=24.31\textrm{ g} $$ where the $\textrm{cm}^3$ label cancels on the left. You can then solve how many cubic centimeters of copper have been added to the graduated cylinder. Convert this volume to mL, and you should find your answer.

Hint: you can calculate the volume of copper, add that to the volume of water, and come up with the total volume.