A cylinder can be considered a circular prism, so finding the surface area is a lot like a regular prism:

- Consider how many sides the shape will have
- Find the area of each side
- Find the sum of the areas

Resources

- Watch the 5 videos and complete your notes:

In-Class Assignment

- p186 #3, 5, 6, 8, 9, 10, 11, 12, 13

Things you should be able to do after today:

- determine the area of a cylinder using its net
- determine the area of a cylinder using a formula
- determine the area of a 3d shape that uses parts of cylinders

Every 3d shape has a surface. The total area of that shape is the surface area. If the 3d shape is a polyhedron (something with flat faces) then it is usually pretty easy to find the total area of the surface:

Resources:

- What is a prism? Watch the Prism Video on Youtube if you're not sure. All the prisms we will be looking at in this course are "right prisms"

Notes:

- Watch the 4 videos shown below and complete your notes before coming to next class.

In Class Assignment:

- HW 5.3 p180 #3-8, 10, 12, 13, 15

Things you should be able to do after today:

- find the area of a rectangle
- find the area of a triangle
- label the measurements on a net of a rectangular or triangular prism
- determine the total surface area of a rectangular or triangular prism

What are other ways to represent a 3d shape in two dimensions? We saw last class that you can use one of several different views, but we can also take the shape and look at its "skin". When you cut a polyhedron along some of its edges to lay it flat, we get a net:

Resources:

- Notes: 5.2 Nets
- Triangular Prism
- Rectangular Prism

Fun Ideas with Nets and Networks

- Polyhedron Nets (paper nets)
- Konigsberg Network Problems - read about Euler's solution to the "bridge" problem and about 4 colour map theory!
- Six Degrees of Separation Network theory was the foundation for the idea that every person in the world is connected by no more than 6 connections. This was popularized in the game "Six Degrees of Kevin Bacon" that appeared in the early 1990's. While designed to be a trivia game, the Oracle of Bacon will quickly find any actor's "Bacon Number" for you.

Pre-Class Assignment:

- Before next class, read through the notes and copy them down into your notebook.
- Think about the following 2 questions:
- Do you think a net is more or less effective at representing a 3d shape two dimensionally than the 3 views?
- Is there a way to figure out how many faces, vertices and edges a shape will have by looking at its net? Use the examples of the triangular prism and the rectangular prism to help you.

In-Class Assignment:

- P173 #3, 4, 6, 7, 8, 9, *12 *13
- Koninsberg Network Problem

You will be introduced to 3d objects as we begin looking at properties of surface area and volume.

Many people who work with blueprints, design or models have to try and show what a 3 dimensional object looks like using only picutres or 2 dimensional diagrams. Consider this computer generated model of a cartoon bird:

This design artist felt that it was very important to have 4 different pictures of the bird when working on it. Think about why there might need to be more than 1 view required to see this 3d object.

Resources:

- 5.1 Notes: Views of 3d Objects
- Video #1: Front, side and top views
- Video #2: Isometric Views
- NCTM Isometric Drawing Tool (if it doesn't load, type in ctrl-F5 which will refresh your browser page. You may need to allow the java program to run on the site)

Assignment to be completed during class:

- 5.1 Practice: p168 #3, 4, 5, 6, 7, 9
- Worksheet on 3d Views

Things you should know after today:

- vocabulary:
- face
- vertex
- edge
- isometric

- the 3 main views for a 3d object
- how to represent a 3d object by drawing the 3 main views and the isometric view
- how to draw an isometric view from the 3 main views
- how to draw the 3 main views from the isometric view
- what the 3 main views will change to look like if the 3d object is rotated in some direction