Track what occupies the space
Capacity is available interior space; water and air partition that space; an immersed solid displaces an equal volume of water. Name every volume before combining it.
Learning goals
- Convert cubic measures, litres and rates consistently.
- Model overflow and water-level rise using displacement.
- Validate capacity, drainage, air-space and remaining-water results.
Concept lesson
Container volume ledger
Separate container capacity, current liquid, air space, immersed object, overflow and remaining liquid; use inner dimensions for capacity when supplied.
Volume-capacity conversions
1 litre=1000 cubic centimetres; 1 cubic metre=1000 litres=1,000,000 cubic centimetres. Convert a rate and a volume to the same unit before multiplying or dividing.
Cube the linear conversion
Because 1 m=100 cm, one cubic metre is 100 cubed cubic centimetres. Capacity conversions follow volume scale, not length scale.
Displacement equations
For full immersion, displaced water volume equals solid volume. In a constant-base container, base area times rise equals displaced volume; overflow equals displacement only when the vessel was initially brim-full.
Drainage rate and tank length
Compute drained litres as rate times minutes, convert to cubic metres, equate it to tank capacity, subtract end-cap volume where necessary and solve the cylindrical length.
Water-level rise
Calculate immersed-solid volume V, calculate the container base area A, then rise delta h=V/A. Add it to the initial water height and compare with the brim.
Water and air below an indicator
Use the indicator height for maximum water volume. Air volume is total internal capacity minus that water volume; convert both to the requested capacity unit.
Unit-normalisation table
List every given value, current unit, target unit and conversion factor before using rates, cost or capacity equations.
Displacement sentence to equation
Translate overflow, immersion or rise wording into V_displaced=V_immersed and A_base times delta h=V_displaced; state whether immersion is complete.
Physical bounds check
Check that water and air sum to capacity, rise does not exceed available height unless overflow is intended, drained volume does not exceed initial contents, and all dimensions are positive.
Immersion-capacity chain
For a composite solid immersed in a partly filled cylinder, calculate displacement, rise, new water level and remaining capacity to the brim, with one consistent unit system and physical checks.
Context equation and validation protocol
Show quantity definitions, unit conversions, governing volume equation, solution and a capacity or physical-bounds check. Answer each requested output separately.
Conversion and displacement mastery
Complete a capacity conversion, an overflow equation, a water-level-rise problem and a remaining-space validation without mixing quantities or units.