A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tin

Question

A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.

Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom.

The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
Increase Decrease No change  The cylinder is replaced with one that has the same density and diameter, but with half the height.
Increase Decrease No change  A liquid with a density of 1.06 g/cm3 is poured into the glass.
Increase Decrease No change  A liquid with a density of 0.76 g/cm3 is poured into the glass.
Increase Decrease No change  More tinted water is added to the glass.
Increase Decrease No change  The cylinder is replaced with one that has the same height and diameter, but with density of 0.89 g/cm3.

Explanation / Answer

1. Increases b/c the diameter is bigger. The overall % of the cylinder underwater and above water is still the same b/c of same density, but since the diameter is bigger, more of it is sticking out

2.No change b/c the height doesn't affect how much it sticks out, (like diameter does), and the density is also still the same

3.Increase b/c water's density is about 1.00 g/cm^3, and the fact that this liquid has a higher density, means that it forms a new layer which raises the cylinder

4.Decreases b/c the liquid added has a lower density than water and the cylinder, so that means that that liquid will be on the top layer, pushing the cylinder down

5.No change b/c the density of the cylinder remains constant, as does the water's density

6.Decrease b/c the density causes it to sink a little more, so it would be more submerged and less would stick out.

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