10.9Surface Area and Volume of Spheres
Quick Answer
Sphere surface area: SA = 4πr². Sphere volume: V = (4/3)πr³. Both formulas depend only on the radius.
Essential Question
How do the surface area and volume formulas for a sphere both depend on the radius, and how do they compare to the formulas for cylinders and cones?
Learning Goals
- 1State the sphere surface area formula SA = 4πr².
- 2State the sphere volume formula V = (4/3)πr³.
- 3Find surface area and volume given the radius or diameter.
- 4Find the radius given the surface area or volume.
- 5Solve applied problems involving spheres.
Key Vocabulary
Sphere
The set of all points in space equidistant from a given point called the center.
Great circle
A cross section of a sphere that passes through the center; the largest possible circle on a sphere.
Hemisphere
Half of a sphere, formed by cutting through the great circle.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.