Question

connecting buoyancy with displacement
metal | density (g/cm³)
aluminum | 2.64
cork | 0.24
iron | 7.50
lead | 11.34
wax | 0.72
which material will displace a volume of water?
dropdown options: all of them, cork and wax, iron, lead, and aluminum, none of them
other dropdowns (partially visible): a volume of water less, a volume of water equal to, a volume of water greater

Explanation:

Step1: Recall Archimedes' Principle

Archimedes' principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. For an object submerged (or partially submerged) in water, the volume of water displaced is related to the object's volume and its density relative to water (density of water is \(1\space g/cm^3\)). Objects with density greater than water (\(1\space g/cm^3\)) will sink and displace a volume of water equal to their own volume. Objects with density less than water will float and displace a volume of water equal to the volume of the submerged part (which has a weight equal to the object's weight). But the question here is about which materials will displace a volume of water (probably meaning fully submerge or displace based on sinking/floating). Let's check densities:

• Aluminum: \(2.64\space g/cm^3>1\), so it sinks, displaces volume equal to its own.
• Cork: \(0.24\space g/cm^3 < 1\), floats, displaces volume less than its own (but still displaces some). Wait, maybe the question is about which will displace a volume equal to their own (sink) or which will displace. Wait, the options: "iron, lead, and aluminum" have densities greater than \(1\space g/cm^3\) (water's density is \(1\space g/cm^3\)), so they will sink and displace a volume of water equal to their own volume. Cork and wax have density less than \(1\), so they float and displace a volume of water equal to the volume of the part under water (which is less than their total volume). But the question is "Which material will displace a volume of water?" Wait, maybe the first dropdown is about which displaces a volume equal to their own (sink). So iron, lead, aluminum have density >1, so they sink, displace volume equal to their own. Cork and wax float, displace less. So the correct option for the first dropdown (assuming the question is which displaces a volume equal to their own) is "iron, lead, and aluminum".

Step2: Analyze each material's density vs water

• Water density: \(1\space g/cm^3\).
• Aluminum (\(2.64\)): \(>1\) → sinks, displaces volume = own volume.
• Cork (\(0.24\)): \(<1\) → floats, displaces volume < own volume.
• Iron (\(7.50\)): \(>1\) → sinks, displaces volume = own volume.
• Lead (\(11.34\)): \(>1\) → sinks, displaces volume = own volume.
• Wax (\(0.72\)): \(<1\) → floats, displaces volume < own volume.

So materials with density >1 (iron, lead, aluminum) will sink and displace a volume of water equal to their own volume. Materials with density <1 (cork, wax) will float and displace a volume of water less than their own volume (but still displace some). But the option "iron, lead, and aluminum" are the ones with density >1, so they will displace a volume of water equal to their own (if the question is about displacing equal to their volume, or just displacing - but since they sink, they displace their full volume).

Answer:

iron, lead, and aluminum