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Honors Geometry

Honors Geometry. Warm- Up: Discovery Activity. Today: 12.1 Questions 12.2 Discovery 12.2 Lesson. 12.2 Surface Area of Prisms and Cylinders Objective: Find lateral areas and surface areas of prisms. Find lateral areas and surface areas of cylinders. Vocabulary:

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Honors Geometry

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  1. Honors Geometry Warm- Up: Discovery Activity Today: • 12.1 Questions • 12.2 Discovery • 12.2 Lesson

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

  3. 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

  4. 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

  5. The lateral area (L) of a right prism isthe 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

  6. Find the lateral area of the regular hexagonal prism. Answer: 360 cm2 • Answer:216 cm2 Example 1

  7. Find the surface area of the rectangular prism. S = 360 cm2 S =416 cm2

  8. 8 cm 5” 9” 3” 3” 5” 2” 20 cm 40” 10” L= 960 cm2 S = 960 + 192√3 cm2 S = 406 in2 Find the surface area of the right regular prisms:

  9. 10’ 40’ L = 2800 ft2 S ≈3526.8 ft2 Find the surface area of the right prism to the nearest tenth of a unit:

  10. 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. circumference circumference h h

  11. The lateral area (L) of a cylinder is equal to the product of the height and the circumference of the base. Lcylinder = 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

  12. Find the lateral area and the surface area of the cylinders. Exact. Round to the nearest tenth. Answer: L = 504π sq. ft. ≈ 1583.4 sq. ft. S = 896π sq. ft. ≈ 2814.9 sq. ft. Answer: L ≈ 1508.0 ft2 S ≈2412.7 ft2

  13. MANUFACTURINGA soup can is covered with the label shown. What is the radius of the soup can? 8 in. 15.7 in. Answer: r ≈ 2.5” Example 4

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

  15. Find the surface area of the composite solids. 10’ 30’ 20” 12” 30” S = 2040 + 216π in2≈ 2719 in2 20’ S = 1050π ft2≈ 3299 ft2

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

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