If a sealed object has a hollow cavity, find the volume occupied by the solid material first. Divide its mass by the density of the material, then subtract that material volume from the external volume.
This method assumes the shell is made of a single material of known density and the contents of the cavity add negligible mass. Keep the density of the material separate from the average density of the whole object.
- Find the external volume from dimensions or displacement.
- Divide mass by material density to find the volume of solid material.
- Subtract the solid volume from the external volume.
Worked example | An aluminium block with an internal cavity
A sealed aluminium block has external dimensions 5.0 cm by 4.0 cm by 3.0 cm. Its mass is 108 g and the density of the aluminium is 2.70 g/cm³. Treat the mass of air in the cavity as negligible.
The external volume is 60 cm³. The aluminium itself occupies 108 ÷ 2.70 = 40 cm³. The cavity occupies 60 − 40 = 20 cm³.
Check the result using average density
The whole object’s average density is 108 ÷ 60 = 1.8 g/cm³. This is below 2.70 g/cm³ because part of the external volume contains air with very little mass.
If you divide the mass by the average density, you get the external volume again. To recover the volume of the shell, use the density of the aluminium.
Try an external volume from water displacement
An object is fully submerged and raises the water reading from 45 cm³ to 85 cm³. Its shell material has density 8.0 g/cm³ and its mass is 240 g. The cavity is sealed and the air mass is negligible. Find the cavity volume.
Answer. The external volume is 40 cm³ and the shell occupies 240 ÷ 8.0 = 30 cm³. The cavity volume is 10 cm³.
Frequently asked questions
Why can’t I use the final measuring-cylinder reading alone?
The final reading includes the water already in the cylinder. Subtract the initial reading to get the displaced volume.
What if the calculated solid volume is larger than the external volume?
Recheck the units, density and mass. Under this model, the material volume cannot exceed the space inside the object’s outer surface.
Official information
SEAB, 2027 SEC G3 Physics syllabus (K323), mass, volume and density. Syllabus checked 11 November 2026. The examples are original.