Topic 3 · IB Maths AA
Volume and surface area of 3D solids
Choose a solid, change its dimensions and rotate it to see how the volume and total surface area formulas respond.
3.0 cm
8.0 cm
Formulas
Try this
- Sphere: set r = 3.0 cm, then r = 6.0 cm. By what factor do V and S change? (Compare with 2³ and 2².)
- Cone: set r = 3.0 cm and h = 4.0 cm. Check that l = 5 cm and that S = 24π cm².
- Composite: explain why S = 3πr² + 2πrh, then compare with a cylinder of the same r and h.
Common error: for a cone or pyramid the curved or sloping faces use the slant height, not the vertical height, so find it with Pythagoras before substituting.