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Geometry HS Mathematics Unit: 10 Lesson: 01 Unwinding the Surfaces of Pyramids and Cones A. Pyramids 1. Look at the template for the octagonal pyramid. What shapes does the net of the right octagonal pyramid include? 2. Cut out the pieces on the template of the right regular octagonal pyramid. Place half of the triangles upright and base-to-base on a sheet of paper. Place the remaining triangles upsidedown in the gaps. Tape the triangles together. a. What type of figure is formed? b. If all the b’s represent the perimeter (P) of the octagonal base, what can be used to represent one side of this new shape? c. What can be used to represent the height of this shape? d. How would the area of this shape be found? 3. What was the shape of the base of the pyramid? How would the area of this shape be found? 4. Write an expression to represent the total surface area of the pyramid? Will this work with all pyramids? ©2012, TESCCC 04/28/13 page 1 of 2 Geometry HS Mathematics Unit: 10 Lesson: 01 Unwinding the Surfaces of Pyramids and Cones B. Cones 1. What shapes does the net of the right cone include? 2. As the number of faces of a pyramid increases, it begins to look like a cone. Think of the lateral surface of the cone as a sector of a circle that can be cut into infinite triangles and rearranged to form a parallelogram. What is the area of the base? 3. What expression could be used to represent the perimeter of the base of the cone? Where is this found on the sector portion of the net? 4. If infinite triangles were arranged into a parallelogram, what would be the length of the base? What would be used to represent the height of the parallelogram? How could the lateral area be expressed? 5. Write a formula for the total surface area of a cone. ©2012, TESCCC 04/28/13 page 2 of 2
