1. Secondary Math 3 8-1 Two and Three-Dimensional Objects

2. Warm Up – Evaluate each sum (Look up formulas in 3.1 and 3.2

3. Slicing or cutting through a three-dimensional figure with a plane can create a two-dimensional shape. For instance, slicing through a cone can create a triangle, circle, parabola, or ellipse. A cone is a three- dimensional figure that has a circle base and a vertex that is not in the same plane as the base. The height of the cone is the perpendicular distance between the vertex and the base.

4. Slicing or cutting through a three- dimensional figure.  Slicing a cone through the vertex creates a triangle.

5. Slicing or cutting through a three- dimensional figure.  Slicing a cone parallel to the base creates a circle.

6. Slicing or cutting through a three- dimensional figure.  Slicing a cone diagonally, through the base, creates a parabola.

7. Slicing or cutting through a three- dimensional figure.  Slicing a cone diagonally creates an ellipse.

8. Videos  https://learnzillion.com/lesson_plans/6699-visualize-cross-sections-of-cones https://learnzillion.com/lesson_plans/6699-visualize-cross-sections-of-cones  https://learnzillion.com/lesson_plans/5012-visualize-cross-sections-of-pyramids https://learnzillion.com/lesson_plans/5012-visualize-cross-sections-of-pyramids  https://learnzillion.com/lesson_plans/8121-visualize-cross-sections-of-prisms https://learnzillion.com/lesson_plans/8121-visualize-cross-sections-of-prisms  https://learnzillion.com/lesson_plans/6900-visualize-cross-sections-of-cylinders https://learnzillion.com/lesson_plans/6900-visualize-cross-sections-of-cylinders  http://www.learner.org/courses/learningmath/geometry/session9/part_c/ http://www.learner.org/courses/learningmath/geometry/session9/part_c/

9. Facts  Whenever a slice is made parallel to the base of the three- dimensional object then the two-dimensional cross-section created will be similar to the base.  The maximum number of sides that a two-dimensional cross-section can have is equal to the number of faces of the three-dimensional figure from which it is sliced.  The two-dimensional cross section will have the same number of sides as the number of intersected faces of the solid.

10. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  Start with a rectangle that has a side on each axis.  What is the area of this shape?

11. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  Rotating around the y-axis creates a right circular cylinder with a height of y and radius of x.

12. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  What is the height?  What is the radius?  What is the volume? Volume of a prism is the area of the base times the height.

13. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  Rotating around the x- axis creates a right circular cylinder with height x and radius y.  Notice that the side perpendicular to the axis of rotation is flat, while the side parallel is curved.

14. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  What is the height?  What is the radius?  What is the volume?

15. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  Rotating a rectangle that has only one side on an axis creates a cylinder with a hole in the middle or a doughnut.

16. Rotating a two-dimensional figure around an axis creates a three dimensional figure.  What is the height?  What is the volume of the figure?

17. Video  https://learnzillion.com/lesson_plans/7269-predict-3d-results-of-rotating-simple- figures https://learnzillion.com/lesson_plans/7269-predict-3d-results-of-rotating-simple- figures

18. Formulas: Rectangular Prism Cylinder Cone Sphere

19. Homework #4-7  4. Horizontal slice.  5. Vertical slice through the vertex opposite the base.  6. Vertical slice not through the vertex opposite the base.  7. Diagonal slice through all four lateral sides and the base.

20. Homework Part B #3  What is the area of the shape?  Describe and sketch the solid created by rotating the shape around the y-axis.  What is the volume of the solid?