LESSON Surface Areas of Pyramids Cones 12 3

LESSON Surface Areas of Pyramids &Cones 12 -3 Honors Geometry Warm-up: Discovery Activity Today: • 12. 2 Homework ? ’s • 12. 3 Discovery • 12. 3 Lesson

LESSON 12 -3 Surface Areas of Pyramids &Cones 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

LESSON 12 -3 Surface Areas of Pyramids &Cones 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

LESSON 12 -3 Surface Areas of Pyramids &Cones 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.

LESSON 12 -3 Surface Areas of Pyramids &Cones The lateral area (L) of a right pyramid is the product of ½ the slant height and the perimeter of the base. Lpyramid = ½Pl 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. Spyramid = L + B = ½Pl + B

LESSON 12 -3 Surface Areas of Pyramids &Cones Find the lateral area of the square pyramid. Answer: 25 cm 2 Answer: 64 in 2

LESSON 12 -3 Surface Areas of Pyramids &Cones Find surface area of the regular pyramids. Round to the nearest tenth. S = 748. 8 cm 2 S =255. 5 cm 2

LESSON 12 -3 Surface Areas of Pyramids &Cones 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

LESSON 12 -3 Surface Areas of Pyramids &Cones 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. Lcone = ½Cl = πrl where C is the circumference of the base, l is the slant height, and is the radius of the base. Scone = L + B = ½Cl + B = πrl + B

LESSON 12 -3 Surface Areas of Pyramids &Cones Find the surface area of the cones. Round to the nearest tenth. S = 20. 2 cm 2 S = 70. 7 cm 2

LESSON 12 -3 Surface Areas of Pyramids &Cones 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

LESSON 12 -3 Surface Areas of Pyramids &Cones 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

LESSON 12 -3 Surface Areas of Pyramids &Cones frustum – a solid formed by cutting the top off of a cone

LESSON 12 -3 Surface Areas of Pyramids &Cones Examples: 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

LESSON 12 -3 Surface Areas of Pyramids &Cones

LESSON 12 -3 Surface Areas of Pyramids &Cones Assignment Due tomorrow: • 12. 3 P. 859 #7 -11 odd, 12, 15, 17, 21 -31 odd, 33, 34 – you must show work including formulas!