8C.5.4 Surface area of a cylinder
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
Pre-Class Assignment:
- Notes Template (8.5.4.notes.cylinder.sa.pdf)
- Watch the 5 videos and complete your notes:
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Leave a comment to answer a question:
- When a hole is drilled through a solid, how can the areas of each part of the cylinder be used to help find the NEW surface area of the new shape (with the hole)?
In-Class Assignment
- p186 #3, 5, 6, 8, 9, 10, 11, 12, 13
8C.5.3 Surface Area
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"
Assignment:
- Watch the 4 videos shown below and complete your notes before coming to next class.
- Blank Notes Template: 8C.5.3 Surface Area
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Leave a comment to answer the question:
- Imagine a 3d shape. If a hole is drilled through from the top to the bottom, will the surface area be larger or smaller?
In Class Assignment:
- HW 5.3 p180 #3-8, 10, 12, 13, 15
- Constructing prisms from nets and finding their surface area
8C.5.2 Nets
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:
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.
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Think about the following 2 questions and add a comment to this article with your answer:
- 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
- Circle Challenge peer editing
