The objectives of this lesson are . . .
- to derive the formulas for surface area of pyramids and cones
- use the concept of netting to help visualize calculations
- practice finding areas of pyramids and cones
- provide additional non-standard practice in problem solving using pyramids and cones
The lesson consists of 5 separate slides shows, two of which provide details about the formulas for the surface area of a cone and a pyramid. The other slide shows provide practice problems and solutions.
Photographs used in this packet were obtained at morguefile.com. Morguefile grants permission to use its images.
The following terms may be new for this lesson:
pyramid - a polyhedron (many sided solid) in which the base is a polygon and the lateral faces (sides) are triangles with a common vertex
cone - has a circular base and a vertex that is not in the same plane as the base
Net - a two-dimensional representation of the faces of a solid (think of cutting it open and unfolding the sides)
Slant height - the altitude of any lateral face of a pyramid (or distance up the side of a right cone)
Source: Geometry; McDougal Littell (2004) by Larson, Boswell, and Stiff
This slide show will demonstrate the formula for the surface area of a pyramid.
Some practice problems and solutions for surface areas of pyramids.
Use trig to find the surface area of a pyramid with a pentagonal base. Up for a challenge??
Now we will turn our attention to cones.
This slide show will demonstrate the formula for the surface area of a cone.
Source: The image for the net of a cone was found at www.mathsteacher.com.au/. ../Image16380.gif
Engage in a battle of wits with the indomitable Mr. Bunny and practice finding surface areas of cones at the same time!