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# Surface area of pyramids and cones

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Author: Dan Bowler
##### Description:

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.

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Tutorial

## New Vocabulary

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

## Surface Areas of Pyramids

This slide show will demonstrate the formula for the surface area of a pyramid.

## Surface Areas of Pyramids Practice

Some practice problems and solutions for surface areas of pyramids.

## Not for the Faint of Heart

Use trig to find the surface area of a pyramid with a pentagonal base. Up for a challenge??

## Cones

Now we will turn our attention to cones.

## Surface Areas of 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

## Surface Areas of Cones Practice Featuring Mr. Bunny

Engage in a battle of wits with the indomitable Mr. Bunny and practice finding surface areas of cones at the same time!