Unit 9: Solid Geometry Lesson 3: Surface Area of Prisms & Cylinders (12.2)
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1 Unit 9: Solid Geometry Lesson 3: Surface rea of Prisms & ylinders (12.2) Learning Targets: 9I raw the net of a prism, and use it to develop a formula for the surface area of a right prism. 9K erive the formula for the surface area of a right cylinder, and use the formula. 9J ind the surface area of a right prism. 9P Solve real world problems involving finding volume or surface area. 9S ind the surface area and volume of a sphere. Standards 8.0 & 9.0 Surface rea sum of LL S think: "when wrapping a present, you wrap all sides" bases two congruent faces Net Unfold your prism think: "peeling a banana" xample of a NT Prism Right Hexagonal Prism lateral faces other faces lateral edges segments connecting the lateral faces Unfold or Peel Net Prism lateral area
2 Investigating Surface rea Prism Goal: ind the surface area using a net prism. (Think "wrapping a present"). irections: 1. opy the net prism (p.727) on a piece of graph paper. Label the sections. 2. ut out the net and fold it along the dotted lines to form a rectangular prism. Investigate: 1. ind the Surface rea: The surface area of a prism is the sum of the area of its faces (base and lateral faces). ind the surface area of the polyhedron. (ach square on the graph paper measures 1 unit by 1 unit). Section Total rea Surface rea = 2. Lay the net flat again and find the following measures: : the area of rectangle (base) = P: the perimeter of rectangle (base) = h: the height of rectangles,,, and = (note: height is perpendicular to the ) 3. Using the values from #2, find: 2 + Ph = 4. ompare #3 and #1 values. What do you notice? Theorem 12.2 Surface rea of a Right Prism Surface rea = sum of Lateral rea + area of 2 bases Surface rea = 2 + L = area of base OR S = 2 + ph L p = perimeter of S xample 1: Surface rea = sum of Lateral rea + 2 bases S = 2 + ph area of base Step 1: ind the area of your base. H G p = perimeter of S Step 2: ind the perimeter of your base. Step 3: ind the height (perpendicular to the base). Step 4: Plug into Surface rea formula.
3 xample 2 G H Step 1: ind the area of your base. Worksheet 6.4 #8 11 all Step 2: ind the perimeter of your base and height (perpendicular to the base). Step 3: Plug into Surface rea formula. xample 3: Surface rea = sum of Lateral rea + 2 bases S = 2 + ph area of base p = perimeter of S xample 4: Surface rea = sum of Lateral rea + 2 bases S = 2 + ph area of base Step 1: ind the area of your base. p = perimeter of S Step 1: ind the area of your base. Step 2: ind the perimeter of your base and height (perpendicular to the base). Step 2: ind the perimeter of your base and height (perpendicular to the base). Step 3: Plug into Surface rea formula. Step 3: Plug into Surface rea formula.
4 xample 5: Surface rea = sum of Lateral rea + 2 bases S = 2 + ph area of base p = perimeter of S 4 ft. Step 1: ind the area of your base. Triangular Prism Worksheet #1 4 3 ft. 2 ft. Step 2: ind the perimeter of your base and height (perpendicular to the base). Step 3: Plug into Surface rea formula. II. ylinder Right ylinder segment joining centers of the bases is II. ylinder Surface rea = sum of 2 bases + lateral area xample 1: a) S = 2πr 2 + 2πrh Take apart a cylinder: Net of a ylinder base areas (circles) lateral areaarea of the curved surface Lateral rea = circumference x height L = 2πrh rea of ases = 2πr 2 b) ind the lateral area of the cylinder. Surface rea = sum of 2 bases + lateral area S = 2πr 2 + 2πrh
5 II. ylinder II. ylinder xample 2: a) xample 3: ind the surface area of a right cylinder that has a diameter of 10 in. and a height of 10 in. b) ind the lateral area of the cylinder. II. ylinder Surface rea = sum of 2 bases + lateral area S = 2πr 2 + 2πrh Worksheet 12.2 Practice #1 8, 12 14, 17 xample 4: ind the height of the cylinder. The radius is 4 cm and the surface area is 160 cm 2. 4
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11. Three-Dimensional Figures Essential Question What is the relationship between the numbers of vertices V, edges E, and faces F of a polyhedron? A polyhedron is a solid that is bounded by polygons, called