GEOMETRY MODULE 3 LESSON 6 GENERAL PRISMS AND CYLINDERS AND THEIR CROSS-SECTIONS

OPENING EXERCISE Complete the opening exercise on page 39 in your workbook. Include the hidden edges.  Is a right rectangular prism hollow? That is, does it include the points inside?

DISCUSSION Right Rectangular Prism: Let E and 퐸’ be two parallel planes.1 Let B be a rectangular region* in the plane E.2 At each point P of B, consider the 푃푃̅̅̅̅̅′ perpendicular to E, joining P to a point 푃′ of the plane 퐸’.3 The union of all these segments is called a right rectangular prism.4 * A rectangular region is the union of a rectangle and its interior.

Definition Review  Lateral Edge  Lateral Face  Base

General Cylinder: Let E and 퐸’ be two parallel planes, let B be a region* in the plane E, and let L be a line that intersects E and 퐸’ but not B. At each point P of B, consider 푃푃̅̅̅̅̅′ parallel to L, joining P to a point 푃′ of the plane 퐸’. The union of all these segments is called a general cylinder with base B. * A region refers to a polygonal region (triangle, quadrilateral, pentagon, and hexagon), a circular region or regions that can be decomposed into such regions.

MOD3 L6 1  Compare the definitions of right rectangular prism and general cylinder. How are they different? The definitions are similar. However, in the right rectangular prism, the region B is a rectangular region. In a general cylinder, the shape of B is not specified. Also, the segments (푃푃̅̅̅̅̅′) in the right rectangular prism must be perpendicular.

Important Notes about Cylinders  If the lateral edges of a general cylinder are perpendicular to the base, the figure is a right figure; if the lateral edges are not perpendicular to the base, the figure is oblique.  A general cylinder is qualified and named by its base. If the base is a polygonal region, then the general cylinder is usually called a prism.  A general cylinder with a disk (circle) for a base is called a circular cylinder.

EXPLORATORY CHALLENGE Use the provided chart to draw each figure under the proper category. Also available on page 45 of your workbook.

DISCUSSION Cross Section vs. Slice

Example of a cross-section of a prism, A general intersection of a plane with where the intersection of a plane with a prism, which is sometimes referred the solid is parallel to the base. to as a slice.

MOD3 L6 2 PRACTICE Which of the slices is also a cross-section? Explain. Only the circle is a cross-section of the cone.

Complete the exercise on page 40 of your workbook. Once completed, sketch the cross-section of each figure on the provided chart.

HOMEWORK Problem Set Module 3 Lesson 6, page 42 #1, #2, #3 use Area = 2휋푟ℎ, #5 Volume of a general cylinder= (푎푟푒푎 표푓 푏푎푠푒)(ℎ푒𝑖푔ℎ푡), and #6. Extra Credit: #11 (This is a physics problem of displacement.) DUE: Tuesday, February 21, 2017

MOD3 L6 3