Unit 10 · Measurement and Three-Dimensional Geometry

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.