What is the volume of an egg?

AA HLAI HLAA SL Solid Also in: Modelling

Research question

How accurately can the volume of a hen's egg be found by modelling its profile with a function and using a volume of revolution, compared with measuring it by water displacement?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

An egg is not an ellipsoid, and mathematicians have published several “egg equations”. Photographing an egg, fitting its profile and integrating to get the volume — then checking with a measuring jug — gives a result you can verify at home.

The mathematics you'll need

Fitting a profile curve (polynomial, ellipse, or a published egg formula)
Volume of revolution V = π∫y² dx (HL)
Numerical integration or technology
Percentage error against displacement

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Photograph 5 eggs side-on on a grid; measure each volume by water displacement in a measuring cylinder.

GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.
Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the idea of a solid of revolution.
Extract profile points and fit two different models.
Integrate to find volumes; compare with displacement.
Test the simple formula V ≈ (π/6)LB² against your results.
Reflect on measurement error in displacement and in the photo.

Pitfalls that cost marks

Rotating about the wrong axis.
Only fitting half the egg without checking symmetry.
Not estimating the uncertainty in the displacement measurement.

Showing personal engagement

Compare egg sizes (S, M, L) with the sizes' official mass ranges.
Try a quail or duck egg.
Design a better approximate formula from your data.

See Criterion C: personal engagement for what examiners look for.

Taking it further

SL students can estimate the volume by summing discs (a Riemann-style approximation) and compare with the exact integral.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).