11.7 ml
The critical thing to note here is the question "Will silver sink or float when places in water?" The reason for this question is that if it sinks, the volume increase will be exactly the volume of the silver. If it floats, then the volume increase will be that of the volume of water the silver displaces. So looking at the density of silver at 10.5 g/cm3, it's a lot denser than that of water which is close to 1 g/cm3. So the silver will sink. Now the question is "What's the volume of 5.35 g of silver?" That number is simply the mass of the silver divided by the density of the silver, giving
volume = 5.25 / 10.5 = 0.5 cm3.
So the volume of silver is 0.5 cubic centimeters. Since a ml is a cubic centimeter, you just need to add up the volume the water with the volume of the silver to get the final answer, giving:
11.2 + 0.5 = 11.7 ml
Note: The exact density of water isn't needed since the volume calculations would be the same regardless. However, if the silver had been less dense than the water, then the exact density of the water would have been needed to calculate how much water would have been displaced.
