M4.5.2 For the adult
Pyramids and cones
Does a cone hold as much as the cylinder it fits inside?
What this chapter teaches
A pyramid or a cone holds one third of the prism or cylinder with the same base and height, so V = ⅓ × base area × perpendicular height. The curved surface of a cone is πrl, with l the slant height from l² = r² + h². The slant height is never used for the volume.
Three questions to ask
There is no one right wording. Listen for the idea.
- How could you show with sand that a cone is one third of a cylinder?
- What is the difference between the perpendicular height and the slant height of a cone?
- Why do you need Pythagoras to find the curved surface of a cone?
After the chapter, the learner can
- Find the volume of a pyramid as 1/3 × base area × height
- Find the volume and curved surface area of a cone
What they copy into their notebook
Pyramid and cone: V = ⅓ × base area × perpendicular height. Cone V = ⅓πr²h. Curved surface πrl, with l² = r² + h². Not the slant height in V.