How will knowing the density of a substance help you determine whether an object made from that material will float in water?

Answer 1

It will not help since what matters is not the density of the material but the amount of water that the shape displaces. If it depended only on the density of the material then metal ships would not float in water.

Answer 2

If an object is to float in water it must displace a volume of water equal to its weight; knowing the density of the substance that makes up the object allow a calculation to be made of the volume of water that must be displaced so that the object will float.

If a substance has a density greater than that of water, it can be made to float by, for example, making it hollow; for example a ship made out of steel can be made to float as it has lots of hollow space inside it which means its effective density is less than that of water. Should the hull be compromised in any way, or by "splashing" over the top, the effective density can increase to the point where it is greater than that of water and the ship will sink.

The density of water is not constant as it depends upon its temperature and things (like salt) dissolved in it; it was this change in density that led to loss of shipping and cargo which prompted the invention of the Plimsoll Line which is marked on the side of ships - it shows where the surface of water will be in different types of sea [water] for a given loading (the Line itself marks the maximum safe load).

However, for small solid objects made of a substance of a greater density than that of water can still be made to float by using the surface tension of water: a clean sewing needle can be made to float if dropped very gently onto some water* as the force provided by the surface tension is enough to prevent the needle from passing through. If the surface tension is disrupted, for example by agitating the water, or by a drop of washing up liquid, the needle will sink.

* If you don't have a steady enough hand: laying the needle on a piece of blotting paper or tissue paper and gently putting the paper on the water will make this easier to achieve - the paper will fairly quickly soak up water and sink away leaving the needle floating on the surface [tension].