10.6Surface Area of Pyramids and Cones
Quick Answer
Regular pyramid: SA = B + ½Pℓ (base + lateral area using slant height ℓ). Right cone: SA = πr² + πrℓ. Both require the slant height, not the vertical height.
Essential Question
Why is the slant height — not the vertical height — used in the surface area formulas for pyramids and cones?
Learning Goals
- 1Define slant height and distinguish it from vertical height.
- 2Apply the surface area formula for a regular pyramid.
- 3Apply the surface area formula for a right cone.
- 4Use the Pythagorean Theorem to find slant height when needed.
Key Vocabulary
Slant height
The distance from the apex to the midpoint of a base edge (pyramid) or to the base circle (cone), measured along the lateral surface.
Regular pyramid
A pyramid with a regular polygon base and apex directly above the center of the base.
Right cone
A cone with its apex directly above the center of the circular base.
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.