Geometry – Chapter 12 Lesson Plans
Section 12.2–Surface Areas of Prisms and Cylinders
Enduring Understandings: The student shall be able to:
- Find the lateral areas and surface areas of prisms and cylinders.
Warm up/Opener:
Standards:
36. Perimeter, Area, and Volume
Finds the lateral and total areas of right prisms, regular pyramids, right circular cylinders, and cones; and finds the surface area of spheres.
Essential Questions: How do we calculate the areas of prisms and cylinders?
Activities:
In a right prism, the lateral edge is also the altitude, and the lateral faces are all rectangles. The lateral edges all form 90 angles with both of the bases.
An oblique prism looks like it is “leaning”. The lateral edge is not the altitude and not all the lateral faces are rectangles.
The lateral area of a solid figure is the sum of the areas of its lateral faces. The surface area of a solid figure is the sum of all the areas of all its surfaces.
A net is a two dimensional shape that can be folded to make the solid figure. Show the net of some shapes. Box manufacturers are very good at nets. They can cut a single piece out of a solid sheet of cardboard and form very sophisticated boxes.
Add extra credit project to research Platonic Solids, find (or make) nets for each, and make the 5 Platonic Solids.
Thm. 12-1: Lateral area of arightprism: L = Ph
Thm 12-2: Surface area of arightprism: S = L + 2B
Thm 12-3: Lateral area of a rightcylinder: L = Ph = 2rh
Thm 12-4: Surface area of a rightcylinder: S = L + 2B = 2rh + 2r2
Summary: For the prism and cylinder, the lateral area is perimeter of base times height, and the surface area is the lateral area plus the area of the two bases.
Assessments:
Do the “Check for Understanding” 1, 3-5
CW WS 11-3 all of the Red Book and 11-2, # 1 & 2 of the Red Book.
HW pg 508-509, # 7 – 23 odd and 20 (10)