# Chapter 11: Geometry and Measurement Relationships

This is the beginning of our chapter on "Geometry and Measurement Relationships". In this chapter, we will:

- Explore the relationship between the dimensions of a cylinder and the dimensions of its net
- Develop and apply a formula for calculating the surface area of a cylinder
- Develop and apply a formula for calculating the volume of a cylinder
- Use diagrams to solve measurement problems
- Investigate the properties of Platonic solids
- Determine the relationship between the number of faces, edges and vertices of a polyhedron (Euler's formula)

If you want to start learning about it right away, there are a couple of units in Khan Academy that will help prepare you. Click on hyperlinks to go to those pages directly. I can't promise that you'll understand everything, but I can promise that if you bring me good questions, I'll do my best to give good answers.

**Sections:**

- 11.1: Exploring Cylinders
- 11.2.1: Surface Area of a Cylinder
- 11.2.2: Surface Area of Platonic Solids
- 11.2.3 Activity: Surface Area and Volume of a Can of Coca-Cola
- Chapter 11 Assignment: Surface Area and Volume of Cylinders
- 11.3: Volume of a Cylinder and Other Platonic Solids
- 11.4: Solving Problems Using Diagrams
- 11.5: Exploring Platonic Solids
- 11.6: Polyhedron Edges, Faces and Vertices

**Prior Knowledge****.** You should already have a good understanding of these subjects. If you don't, now is a good time to brush up on your skills.

- Perimeter and Area of Triangles. This section helps study the difference between perimeter and area for various shapes. Here are helpful sections for grade 8 students.
- Perimeter and Area: The Basics. Good explanation of the basics of perimeter and area.
- Triangle Area Proofs. Explains where the triangle area formula $latex A_{triangle} = \frac{bh}{2}$ comes from. The guy explains this for grade 10 students, so don't feel bad if you don't understand everything he's saying.
- Area of Triangles. This is a problem-solving section. Try some to see if you understand how to find the area and circumference of triangles.
- Area of Triangles 2. This section is harder. You have to either know Heron's Formula or the Pythagorean Theorem for some of the questions. Only try this if you want a challenge.

**Cahier Evaluations**

At the end of this unit, we will be evaluating students' work by observing their chairs. Here are the success criteria.