The density of an object is equal to mass over volume.

Knowing the length and the cross sectional area of the log, we can find its volume.

Plugging in volume and mass into the equation will enable us to find density.

The formula for density is:

In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.

Now that we know both masses, we can find the difference.

Solution A and solution X have the same concentration, therefore, we are only concerned with temperature differences between the two solutions. Density is dependent on temperature: as temperature increases density decreases. Recall the definition of density:

Increasing the temperature will slightly increase the volume of the solution and, subsequently, decrease density. The temperature has no effect on mass. The solution at the higher temperature (solution X) will have a lower density.

Plotted in this way, the slope of the line is equal to the density of the substance.

We would expect the line to be linear and positive. A slope close to zero could indicate that the data was not graphed optimally or that the density is extremely small, and a density greater than one is possible (anything that sinks in water has a density greater than one). A negative density would indicate that greater masses of this substance have smaller volumes, which, for a pure substance, does not make sense.

Solving this question requires that we use the given densities to convert mass to volume.

We see that only the aluminum sample has a volume over three liters.  

Specific gravity is the density of the substance over the density of water.

Density is given by mass over unit volume.

A boat with a mass of 6000kg and a volume of 10m³ will have a density of 600 kg/m³.

If the object is at rest, the net force on it must equal 0. At any point in the liquid, the total downwards force is described as the difference between the gravitational force and bouyant force: . When the object is not accelerating, this reduces to .

Plugging in the equations for these forces respectively yields .

Since mass is the product of density and volume, .

Note that in this case the object's volume equals the volume of liquid displaced, since the object is completely submerged. So, the volumes on either side cancel, as does gravity, leaving just .

The density of ice is less than that of water (density of ice = 0.92 g/cm³, density of water = 1 g/cm³). Ice will only sink in liquids that are less dense than 0.92 g/cm³. Since ice will only sink in liquids that are less dense than water, the unknown liquid must have a lower density than that of water.

The slope of the solid/liquid phase transition line can predict the comparative density of the solution in each section. A negative slope indicates that the solid phase is less dense than the liquid phase. A positive slope indicates that the solid is more dense. In the above phase diagram, the slope is negative, indicating that the solid is less dense than the liquid. 

To solve, we can equate the volume of the gasoline displaced to the volume of the portion of the object that is submerged.

We know that of the object is submerged, thus of the object's total volume will equal the volume of water displaced.

The displaced masses are equal.