Learning pack · IGCSE handout

Volume

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Volume measures space in 3D: prisms (including cylinders) use area of cross-section × length.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 12_volume_handout.pdf · 12_volume_handout_answers.pdf

Full topic summary

Volume measures space in 3D: prisms (including cylinders) use area of cross-section × length.

Key learning points

Cuboid $lwh$ ; prism $A_{\text{cross}}\times\text{length}$ ; cylinder $\pi r^2 h$ .
Composite solids: add/subtract known volumes.
Capacity in litres: $1000\,\mathrm{cm}^3=1\,\mathrm{l}$ .

Worked example 1 — Cuboid

Cuboid $5\times3\times2$ . Volume?

Working

V=30

Length × width × height.

Worked example 2 — Cylinder

Radius $3$ , height $10$ . Volume in terms of $\pi$ ?

Working

V=\pi r^2 h=90\pi

Base area × height.

Worked example 3 — Prism

Cross-section area $12$ , length $7$ . Volume?

Working

V=84

Area × length.

Worked example 4 — Cone volume

Radius $3$ , height $4$ . Volume of cone in terms of $\pi$ ?

Working

V=\tfrac{1}{3}\pi r^2 h=12\pi

One-third of the enclosing cylinder.

🎬 Topic videos

Strange Spheres in Higher Dimensions - Numberphile
Numberphile · 11 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
The Best Way to Pack Spheres - Numberphile
Numberphile · 12 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Calculating the optimal sphere packing density: with oranges
Stand-up Maths · 23 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Volume and Capacity (Converting between units of volume)
Eddie Woo · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Volume of a Sphere
Eddie Woo · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Volumes of Prisms & Cylinders
Eddie Woo · 7 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

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