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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
GM6-3
New NZC (2026)
NZC26-P4-MEA-MEA-K-Y10-05
Resources
- CorbettMaths worksheet on the volume of a coneQuestions PDF · Answers
- CorbettMaths worksheet on the volume of a pyramidQuestions PDF · Answers
- CorbettMaths worksheet on the volume of a sphereQuestions PDF · Answers
Terminology
- pyramid
- cone
- sphere
- volume
- base area
- perpendicular height
- radius
- in terms of pi
- scale factor
Task goals
- Find the volume of a cone, square pyramid, or rectangular pyramid using the correct formula.
- Find the volume of a sphere or hemisphere, keeping the answer in terms of pi where appropriate.
- Find a cone's perpendicular height from its radius and slant height using Pythagoras' theorem before finding the volume.
- Rearrange a volume formula to solve reverse problems (given the volume, find a missing radius, height, or base side length).
- Apply the k-cubed scale-factor rule when every length of a solid is multiplied by a constant.
- Find the total volume of a composite solid made of two joined shapes (e.g. a hemisphere joined to a cone).
Where this fits
What leads into this objective, and where it goes next.
Before
Measurement applications: compound 3D shapes
Nets
Area, Perimeter and Circumference of 2D Shapes
You are here
Volume of pyramids, cones, and spheres
Know
The general formula for the volume of a prism is V = Al, where A is the consistent cross-sectional area and l is perpendicular to the plane of the cross-sectional area.
Statement▸
Year 10 · Measurement · Measuring
NZC26-P4-MEA-MEA-K-Y10-05
Also under GM6-3:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.