LESSON Today: 12.1 Questions 12.2 Discovery 12.2 Lesson Warm- Up: Discovery Activity

LESSON 12.2 Surface Area of Prisms and Cylinders Objective: 1.Find lateral areas and surface areas of prisms. 2.Find lateral areas and surface areas of cylinders. Vocabulary: lateral face, lateral edge, base edge, altitude, height, lateral area, axis, composite solid

LESSON polyhedra polyhedra – solids with flat polygon faces and the segments of intersection are called edges prism – a polyhedron with 2 parallel congruent faces and parallel edges that connect corresponding vertices – named by the base base – 2 parallel and congruent faces lateral edges – parallel lines joining corresponding vertices of the bases lateral face – non-base sides

LESSON right prism – a prism where the lateral edges are perpendicular to the bases (does not mean the bases have right angles) regular prism – a prism with bases that are regular lateral surface area ( L ) – the sum of the areas of the lateral faces total surface area ( S )– the sum of the prism’s lateral area and the areas of the two bases

LESSON The lateral area (L) of a right prism is the product of the height and the perimeter of the base. L = Ph P is the perimeter of the base and h is the height of the prism. The total area of a prism is the sum of the prism’s lateral area and the areas of the two bases. S = L + 2B

LESSON Example 1 Answer: 360 cm 2 Find the lateral area of the regular hexagonal prism. Answer: 216 cm 2

LESSON S = 360 cm 2 Find the surface area of the rectangular prism. S =416 cm 2

LESSON Find the surface area of the right regular prisms: 20 cm 8 cm L = 960 cm 2 S = √3 cm 2 40” 5” S = 406 in 2 9” 3” 2” 5” 10”

LESSON Find the surface area of the right prism to the nearest tenth of a unit: L = 2800 ft 2 S ≈ ft 2 10’ 40’

LESSON cylinder – A cylinder resembles a prism in having two congruent parallel bases. The bases of the cylinder, however, are circles. *cylinder implies right cylinder cylinder‘s lateral area is a rectangle with a base equal to the circumference of the base and a height equal to the height of the cylinder. h circumference h

LESSON The lateral area (L) of a cylinder is equal to the product of the height and the circumference of the base. L cylinder = Ch = 2πrh C is the circumference, h is the height of the cylinder and r is the radius of the base. The total area of a cylinder is the sum of the cylinder’s lateral area and the areas of the two bases (circles). S = L + 2B

LESSON Find the lateral area and the surface area of the cylinders. Exact. Round to the nearest tenth. Answer: L = 504π sq. ft. ≈ sq. ft. S = 896π sq. ft. ≈ sq. ft. Answer: L ≈ ft 2 S ≈ ft 2

LESSON Example 4 MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can? 8 in in. Answer: r ≈ 2.5”

LESSON Example 4 A.12 inches B.16 inches C.18 inches D.24 inches Find the diameter of a base of a cylinder if the surface area is 480  square inches and the height is 8 inches.

LESSON Find the surface area of the composite solids. S = π in 2 ≈ 2719 in 2 30” 20” 12” 20’ 10’ 30’ S = 1050π ft 2 ≈ 3299 ft 2

LESSON Assignment Due tomorrow: 12.2 P. 850 #9-33 odd, 43 – you must show work including formulas!