Geometry 7­4 Surface Area Cylinders.notebook Surface Area ­ Cylinder Geometry • Students will use the net of a cylinder to determine formulas for total and lateral surface of a cylinder. Find the surface area of the prism. • Students will write, solve and model equations involving surface 1. 2. 7 m area of a cylinder. 4 m 4 TEKs 3. in 6 m 8.7B ­ Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders Identify the pair of angles. 3. x 4. x y answer y 1. 96 units2 4. 2. 188 units2 The surface area of a rectangular prism 3. 158 in 2 4. C is 25 ft2. If each side is tripled, what is the new area? 70o 35o 25 225 75o 90o 50 75 Title Page Warm­Up 1. A = 8 • 5 = 40 in.2; 2 • 8 • 5 = 80 in.2 Practice Answers 2. A = 5 • 3 = 15 in.2; 2 • 5 • 3 = 30 in.2 3. A = 8 • 3 = 24 in.2; 2 • 8 • 3 = 48 in.2 Maintain Your Skills 4. S = 80 + 30 + 48 = 158 in.2; 158 in.2 5. 158 in2 1. A 2. D 6. 340 in2 7. 48 cm2 8. 88 in.2 9. 152 in2 10. 4 cubes 11. The surface area will be 4 times as great. Sample answer: Since you are finding area and you multiply each dimension by 2, the area will be multiplied by 2 × 2, or 4. Homework Answers Math Humor What is the best dessert in the Math Teacher's Cafe? A slice of cherry pi. How many bases? How many lateral surfaces? What is the word that describes how much the can holds? What is the word that describes the paper label? Math Humor Introduction 1 Geometry 7­4 Surface Area Cylinders.notebook How many squares are in the rectangle and 2 circles? Cut and tape Labsheet in your journal Milton’s Chocolate Factory is creating a new package for their 3.0 chocolate candies. They are considering a cylinder as shown. Move to check your answer. 1. Determine the surface area using the net. Area Top Circle (πr2): 3.14 x 1.52 = 7.065 Area Bottom Circle (πr2): 3.14 x 1.52 = 7.065 Area Top Circle (πr2): ________________ Pull Pull Circumference (2rπ): 2 x 1.5 x 3.14 = 9.42 Area Bottom Circle (πr2): ________________ Area Lateral (C)(h): 9.42 x 10 = 94.2 Circumference (2rπ): ________ TOTAL: 108.33 cm2 Area Lateral (C)(h): __________________ TOTAL (Add Areas): 1 8 15 ≈29 2. Determine the surface area using the formula. 1 2 2 9 16 Radius: _____________________ Height of prism: ______________ 3 4 3 10 17 TOTAL: 11 18 4 S = 2 πrh + 2 πr2 5 19 12 1 2 Radius Radius 3 4 height 6 13 20 7 14 21 Introduction Labsheet Only be able to whisper... or only be able to shout? Find a friend and them how to find the difference between a prism and a cylinder. Friend Transition Would You Rather? _____ Surface Area Cylinders 2. How to find • from a net ­ find area of Date the surface all sides and add area of a 1. What is the • sum of area of 2 circular • from the formula cylinder? surface area bases & lateral surface S = 2 πrh + 2 πr2 of a cylinder? 3 m Radius height Radius • answer in units 5 m squared 2(π x 3 x 3) + (6 x π x 5) lateral surface = 18π + 30π = 48π = 56.52 + 94.2 = 150.72 m2 Notes Notes 2 Geometry 7­4 Surface Area Cylinders.notebook 3. What is • how total area changes changing dimensions? • radius has bigger impact than height S = 2 πrh + 2 πr2 doubles doubles quadruples 4 in 2 in 3 in 9 in Pull Pull Notes Application How many faces? d = 3 in d = 2 ft r = 1 cm Practice area area area Surface Area of circumference circumference circumference Cylinders Worksheet r = 3 m d = 1yd area area circumference circumference Activity Homework Closing Questions What is the formula for area of a circle? (A = πr2) What is the lateral surface? (Circumference x height) Closing Questions 3.