Density: Question 10

Worked solution

Part (a): Average density of the buoy

The average density uses the total mass of the buoy and its total external volume, not the volume of plastic alone:

$\rho_{\text{avg}} = \frac{m}{V} = \frac{850\text{ g}}{2400\text{ cm}^3}$

$\rho_{\text{avg}} = 0.35416\ldots\text{ g/cm}^3$

To 3 significant figures:

$\rho_{\text{avg}} = \boxed{0.354\text{ g/cm}^3}$

Part (b): Is this consistent with floating?

Compare the buoy’s average density with the density of seawater:

$0.354\text{ g/cm}^3 < 1.03\text{ g/cm}^3$

Since the buoy’s average density is less than the density of seawater, this is consistent with the buoy floating.

Part (c): Why the buoy floats despite the plastic being denser than seawater

The buoy is not solid plastic all the way through (most of its total volume is a sealed, empty air space, which adds a large amount of volume but almost no extra mass. This makes the buoy’s average density (total mass ÷ total external volume) much lower than the density of the plastic material itself ($1.40\text{ g/cm}^3$). Because this average density ($0.354\text{ g/cm}^3$) is lower than the density of seawater, the buoy floats) even though the solid plastic it is made from would sink if it had no hollow space.

Final answers

• (a) Average density $=$ $0.354\text{ g/cm}^3$
• (b) Yes, $0.354\text{ g/cm}^3 < 1.03\text{ g/cm}^3$, consistent with floating.
• (c) The enclosed air adds volume with negligible mass, so the buoy’s average density is far below both the plastic’s own density and the density of seawater.