M4.5.3 For the adult
Spheres
How much air is in a football, and how much leather covers it?
What this chapter teaches
A sphere that just fits in a cylinder fills two thirds of it, so V = 4/3 πr³. Its surface area is 4πr², the curved area of that cylinder. A half sphere has half the volume. Its curved surface is 2πr², and with the flat face it is 3πr².
Three questions to ask
There is no one right wording. Listen for the idea.
- What is the cylinder that just holds a sphere, and how tall is it?
- If the radius of a ball doubles, what happens to its volume and to its surface area?
- When we ask for the surface of a half sphere, why do we need to say whether the flat face counts?
After the chapter, the learner can
- Find the volume and surface area of a sphere
- Find the volume of a half sphere
What they copy into their notebook
Sphere: V = 4/3 πr³, A = 4πr². Half sphere: V = 2/3 πr³, curved surface 2πr², with the flat face 3πr². Radius doubles, volume × 8.