1. Volume of Prisms, Cross Sections and Scale Factors
Amount of space the can fill a 3D figure

2. Warm-up
A regular decagon has a perimeter of 150 in. and an apothem of What is the area of this polygon to the nearest tenth of a square inch?
Calculate area of a triangle with triangle apothem = 14 in and side = in
Calculate the area of an octagon with octagon apothem = 14.1 cm and side = 11.7 cm

3. Quiz Classify you need three things, angles, sides and triangle
Naming a quad based on definition
Showing work that is easy to follow
Labeling answers
First problem on the back people forgot the divide by 2
Other problems for parallelograms and rectangles students divided by 2, know your formulas

4. How do you calculate volume
Area of the base times the height Height still needs to be perpendicular

5. Examples

6. Volume vs SA
If each cube is 1 cubic unit what is the volume of this figure If I have 24 unit cubes what are all the different rectangular prisms that could be formed, how do you know this is all of them What is the surface area of each prism? What do you notice? It gets closer to a cube, same volume but smaller SA

7. Cubes
Cubes would give you the smallest surface area for the volume with rectangular prisms If you are give the unit cubes needed for a prism how can you determine the length of each side I want 64 unit cubes, what would be the length of each side of the cube

8. Cross Section
When you cut a figure what new 3D figures do you gets and what 2D figures are formed. This can depend on how you cut the figure

9. Examples
How could you cut each of the following prisms into a square prism, not a cube.
A triangular prism
A pentagonal prism
Hexagonal prism

10. Examples What are the shapes of the two resulting figures?
What are the shapes of the faces of the figures?
How many vertices, edges, and faces does each of the figures have?

11. Scale Factor and Changing Areas
Suppose that a company sells laundry soap in boxes that measure 4 in by 8 in by 12 in. The company wants to offer larger economy sized boxes.
What is the SA and volume of this given box
What changes in dimensions would give a box with double the volume?
What changes in dimensions would give a box with triple the volume?
What changes in dimensions would give a box with half the volume?

12. Scale Factor
Given the following scale factors find the new dimensions, new volume and new SA of the box
Scale Factor 2
Scale factor 3
Scale factor 1.5 or 3/2
Scale factor of .5 or ½
What patterns do you notice?

13. Scale Factor
Scale factor is equal to ration of perimeters when setting up a proportion Scale factor squared is equal to the ratio of areas when setting up a proportion, this is also surface area Scale factor cubed is equal to the ratio of volumes when setting up a proportion