Surface Area and Volume


Several types of three-dimensional objects are reviewed or introduced in this chapter, and ways to calculate their surface areas and volumes are introduced.  Euler’s Formula, nets, latitude and longitude, and perspective drawings are all related to three-dimensional objects.  There is also a discussion of non-Euclidean geometries, including spherical geometry.

What you can expect to learn

After completing these activities you should be able to

  1. Apply Euler’s Formula to polyhedra.
  2. Draw cross sections and nets of three-dimensional figures.
  3. Derive and apply formulas for the surface areas of cylinders, cones, and spheres.
  4. Derive and apply formulas for the volumes of cylinders, cones, and spheres.
  5. Apply the geographical coordinate system of latitude and longitude.
  6. Contrast spherical geometry with Euclidean geometry.
  7. Sketch three-dimensional figures using various perspective techniques.
  8. Recognize geometry as a powerful problem-solving tool that is limited when solving moral issues.
Activity List