1. LESSON Today: 12.2 Homework ?’s 12.3 Discovery 12.3 Lesson Warm-up: Discovery Activity

2. LESSON 12.3 Surface Areas of Pyramids and Cones Objective: 1.Find lateral areas and surface areas of pyramids. 2.Find lateral areas and surface areas of cones. Vocabulary: regular pyramid, slant height, right cone, oblique cone, frustum

3. LESSON pyramid – one polygon base with non-parallel lateral edges that meet at a single point. They are named by their base. regular pyramid – a pyramid whose base is a regular polygon and lateral faces are all congruent isosceles triangles. lateral face – non-base sides

4. LESSON altitude – perpendicular segment from the vertex to the base. slant height ( l ) – perpendicular segment from the vertex to a side of the base. lateral edge – segment from vertex to a vertex of the base. right pyramid – a pyramid whose altitude intersects the center of the base. oblique pyramid – altitude whose altitude does not intersect the center of the base.

5. LESSON The lateral area (L) of a right pyramid is the product of ½ the slant height and the perimeter of the base. L pyramid = ½P l P is the perimeter of the base and h is the height of the prism. The total area of a pyramid is the sum of the prism’s lateral area and the areas of its base. S pyramid = L + B = ½P l + B

6. LESSON Example 1 Answer: 25 cm 2 Find the lateral area of the square pyramid. Answer: 64 in 2

7. LESSON S = 748.8 cm 2 Find surface area of the regular pyramids. Round to the nearest tenth. S =255.5 cm 2

8. LESSON Find to the nearest square inch the lateral area and the total surface area of a 100” high regular pyramid with an octagon base of sides 20”. L = 8,230 in 2 S = 10,161 in 2

9. LESSON cone – A cone resembles a pyramid, but its base is a circle. *cone implies right cone The lateral area of a cone is equal to one-half the product of the slant height and the circumference of the base. L cone = ½C l = πrl where C is the circumference of the base, l is the slant height, and is the radius of the base. S cone = L + B = ½C l + B = πrl + B

10. LESSON S = 20.2 cm 2 Find the surface area of the cones. Round to the nearest tenth. S = 70.7 cm 2

11. LESSON ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of 2.5 inches. Find the lateral area of the sugar cone to the nearest tenth of an inch. S = 31.8 in 2

12. LESSON HATS A conical birthday hat has an altitude of 6 inches and a diameter of 4 inches. Find the lateral area of the birthday hat. S = 39.7 in 2

13. LESSON frustum – a solid formed by cutting the top off of a cone

14. LESSON Find the total area of a frustum if the radii of the top and bottom bases are 4 and 8 respectively, and the slant height is 5. 140 u 2 A tower is made up of a cylinder with a cone on top of it. If the radius of the cylinder and cone are 4 m, the height of the cylinder is 7 m and the slant height of the cone is 5 m, find the total area of the tower. 92 m 2 Examples:

15. LESSON Concept

16. LESSON Assignment Due tomorrow: 12.3 P. 859 #7-11 odd, 12, 15, 17, 21-31 odd, 33, 34 – you must show work including formulas!