Surface Areas of Cylinders ACTIVITY: Finding Surface Area. ACTIVITY: Finding Area. How can you find the surface area of. a cylinder?

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1 9.3 Suface Aeas of Cylindes a cylinde? How can you find the suface aea of A cylinde is a solid that has two paallel, identical cicula s. lateal suface h 1 ACTIVITY: Finding Aea Wok with a patne. Use a cadboad cylinde. Talk about how you can find the aea of the outside of the oll. Estimate the aea using the methods you discussed. Use the oll and the scissos to find the actual aea of the cadboad. cm in Compae the actual aea to you estimates. 2 ACTIVITY: Finding Suface Aea Wok with a patne. Geomety In this lesson, you will find suface aeas of cylindes. Make a net fo the can. Name the shapes in the net. Find the suface aea of the can. How ae the dimensions of the ectangle elated to the dimensions of the can? 368 Chapte 9 Suface Aea and Volume

2 3 Math Pactice View as Components ACTIVITY: Estimation Wok with a patne. Fom memoy, estimate the dimensions of the eal-life item in inches. Then use the dimensions to estimate the suface aea of the item in squae inches. a. b. c. How can you use the esults of Activity 2 to help you identify the components of the suface aea? d. 4. IN YOUR OWN WORDS How can you find the suface aea of a cylinde? Give an example with you desciption. Include a dawing of the cylinde. 5. To eight decimal places, π Which of the following is closest to π? a b. To appoximate Ƽ , I simply emembe 1, 1, 3, 3, 5, 5. c. Then I compute Ƽ Use what you leaned about the suface aea of a cylinde to complete Execises 3 5 on page 372. Section 9.3 ms_ed pe_0903.indd 369 Suface Aeas of Cylindes 369 2/2/15 9:16:10 AM

3 9.3 Lesson Lesson Tutoials Remembe Pi can be appoximated as 3.14 o Suface Aea of a Cylinde Wods The suface aea S of a cylinde is the sum of the aeas of the s and the lateal suface. 2 h lateal suface h Algeba S = 2π 2 + 2π h Aeas of s Aea of lateal suface EXAMPLE 1 Finding the Suface Aea of a Cylinde 4 mm 3 mm Find the suface aea of the cylinde. Round you answe to the neaest tenth. Daw a net. S = 2π 2 + 2π h 4 mm = 2π (4) 2 + 2π (4)(3) = 32π + 24π = 56π The suface aea is about squae millimetes. 4 mm 3 mm Execises 6 8 Find the suface aea of the cylinde. Round you answe to the neaest tenth yd 2. 3 cm 9 yd 18 cm 370 Chapte 9 Suface Aea and Volume

4 EXAMPLE 2 Finding Suface Aea How much pape is used fo the label on the can of peas? Find the lateal suface aea of the cylinde. S = 2π h Do not include the aeas of the s in the fomula. 1 in. 2 in. = 2π (1)(2) Substitute. = 4 π Multiply. About squae inches of pape is used fo the label. EXAMPLE 3 Real-Life Application 5.5 in. 2 in. You ean $0.01 fo ecycling the can in Example 2. How much can you expect to ean fo ecycling the tomato can? Assume that the ecycle value is popotional to the suface aea. Find the suface aea of each can. Tomatoes S = 2π 2 + 2π h Peas S = 2π 2 + 2π h = 2π (2) 2 + 2π (2)(5.5) = 2π (1) 2 + 2π (1)(2) = 8 π + 22π = 2π + 4 π = 30π = 6 π Use a popotion to find the ecycle value x of the tomato can. 30 π in. 2 x 6π in.2 = $0.01 suface aea ecycle value 30π 0.01 = x 6 π Coss Poducts Popety = x Divide each side by 6π = x Simplify. You can expect to ean $0.05 fo ecycling the tomato can. Execises WHAT IF? In Examples 2 and 3, the height of the can of peas is doubled. a. Does the amount of pape used in the label double? b. Does the ecycle value double? Explain. Section 9.3 Suface Aeas of Cylindes 371

5 9.3 Execises Help with Homewok 1. CRITICAL THINKING Which pat of the fomula S = 2π 2 + 2π h epesents the lateal suface aea of a cylinde? 2. CRITICAL THINKING You ae given the height and the cicumfeence of the of a cylinde. Descibe how to find the suface aea of the entie cylinde. 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-1)= Make a net fo the cylinde. Then find the suface aea of the cylinde. Round you answe to the neaest tenth ft 2 ft 4. 4 m 5. 1 m 7 ft 5 ft 1 Find the suface aea of the cylinde. Round you answe to the neaest tenth mm 7. 6 ft cm 2 mm 7 ft 6 cm 2 Find the lateal suface aea of the cylinde. Round you answe to the neaest tenth in ft 14 m 6 ft 4 in. 2 m 12. ERROR ANALYSIS Descibe and coect the eo in finding the suface aea of the cylinde. 5 yd 10.6 yd S = π 2 + 2πh = π(5) 2 + 2π(5)(10.6) = 25π + 106π = 131π yd 2 50 ft 13. TANKER The tuck s tank is a stainless steel cylinde. Find the suface aea of the tank. adius 4 ft 372 Chapte 9 Suface Aea and Volume

6 14. OTTOMAN What pecent of the suface aea of the ottoman is geen (not including the bottom)? 16 in. 15. REASONING You make two cylindes using 8.5-by-11-inch pieces of pape. One has a height of 8.5 inches, and the othe has a height of 11 inches. Without calculating, compae the suface aeas of the cylindes. 6 in. 8 in. 16. INSTRUMENT A ganza is a pecussion instument used in samba music. a. Find the suface aea of each of the two labeled ganzas. b. The weight of the smalle ganza is 1.1 pounds. Assume that the suface aea is popotional to the weight. What is the weight of the lage ganza? 17. BRIE CHEESE The cut wedge epesents one-eighth of the cheese. a. Find the suface aea of the cheese befoe it is cut. 3.5 cm b. Find the suface aea of 5.5 cm the emaining cheese afte the wedge is emoved. Did the suface aea incease, decease, o emain the same? 18. Repeated Reasoning A cylinde has adius and height h. 10 cm 24.5 cm a. How many times geate is the suface aea of a cylinde when both dimensions ae multiplied by a facto of 2? 3? 5? 10? b. Descibe the patten in pat (a). How many times geate is the suface aea of a cylinde when both dimensions ae multiplied by a facto of 20? h 3 in. 1 in. Find the aea ft (Skills Review Handbook) cm in. 5 in. 5 ft 8 cm 12 in. 22. MULTIPLE CHOICE 40% of what numbe is 80? (Section 6.4) A 32 B 48 C 200 D 320 Section 9.3 Suface Aeas of Cylindes 373