Volume 2: Pyramids, Cones, and Spheres
Master volumes of pyramids, cones, and spheres in MYP Maths Year 5 Standard. Formulae, common errors, composite shapes, and MYP exam question guidance included.
Building on Volume 1
Volume 2 extends the prism and cylinder work from Volume 1 into three new shapes: pyramids, cones, and spheres. Each formula introduces a fraction that students often misapply, so careful substitution and clear working are essential.
Key Formulae
- Volume of a pyramid: V = ⅓ × base area × height
- Volume of a cone: V = ⅓πr²h
- Volume of a sphere: V = (4/3)πr³
Connecting to Volume 1
A cone has exactly one-third the volume of a cylinder with the same radius and height. A pyramid has one-third the volume of the corresponding prism. Understanding this relationship helps students check whether their answers are reasonable and builds conceptual depth beyond formula recall.
What Students Learn to Do
Students calculate volumes of standalone shapes, find missing dimensions given the volume, and begin working with composite 3D objects that combine shapes from both Volume 1 and Volume 2. They also practise converting between units of volume (cm³ to m³, for example).
Common Mistakes
- Forgetting the ⅓ factor for cones and pyramids
- Cubing the radius for spheres but squaring it instead
- Using the slant height of a cone instead of the perpendicular height
- Not squaring or cubing correctly when units are converted
MYP Question Style
Higher-demand Criterion A questions may present a composite shape — for example, a cylinder topped with a hemisphere — and ask for total volume or surface area. Students must identify which formulae apply to each component and combine results correctly.
Practice Approach
Learn each formula individually first. Then practise composite shapes where one component is a prism or cylinder and the other is a pyramid, cone, or hemisphere. Reverse problems (finding radius given volume of a sphere, for instance) are also worth practising before assessments.