6.3 Surface Areas Of Cylinders - Big Ideas Learning
English6.3SpanishSurface Areas of CylindersHow can you find the surface area ofSSTATESTANDARDSa cylinder?MA.7.G.2.11ACTIVITY: Finding AreaWork with a partner. Use acardboard cylinder. Talk about how you can find thearea of the outside of the roll. Use a ruler to estimate the areaof the outside of the roll. CutCut the roll and press it out flat.Then find the area of the flattened cardboard. How close isyour estimate to the actual area?BaserLateralsurfacehThe surface area of a cylinder is the sum ofthe areas of the bases and the lateral surface.Base2ACTIVITY: Finding Surface AreaWork with a partner.262Chapter 6 Trace the top and bottom of a can on paper. Cut out thetwo shapes. Cut out a long paper rectangle. Make the width the sameas the height of the can. Wrap the rectangle around thecan. Cut off the excess paper so the edges just meet. Make a net for the can. Name the shapes in the net. How are the dimensions of the rectangle related to thedimensions of the can? Explain how to use the net to find the surface area ofthe can.Surface Areas of Solids
EnglishSpanish3ACTIVITY: EstimationWork with a partner. From memory, estimate the dimensions of the real-lifeitem in inches. Then use the dimensions to estimate the surface area of theitem in square inches.b.a.c.d.4. IN YOUR OWN WORDS How can you find the surface area of a cylinder?Give an example with your description. Include a drawing of the cylinder.5. To eight decimal places, π 3.14159265. Which of the following isclosest to π ?a. 3.14227355113b. —“To approximate the irrationalnumberƼ 3.141593, I simplyremember 1, 1, 3, 3, 5, 5.”c. —“Then I compute the rationalnumberƼ 3.141593.”Use what you learned about the surface area of a cylinder tocomplete Exercises 5 – 7 on page 266.Section 6.3Surface Areas of Cylinders263
English6.3SpanishLessonLesson TutorialsCircumference, C 2π rArea, A π r 2The diagram reviews someimportant facts for circles.Radius, rSurface Area of a CylinderWordsThe surface area S of a cylinder is the sum of the areas of thebases and the lateral surface.BaseRememberrrcircumferenceπ ——diameter2π rhLateral surfacePi can be approximated22as 3.14 or —.7AlgebrahS 2π r 2 2π rhrArea ofbasesEXAMPLE1Area oflateral surfaceBaseFinding the Surface Area of a CylinderFind the surface area of the cylinder. Round your answer to thenearest tenth.4 mm3 mmDraw a net.S 2π r 2 2π rh4 mm 2π (4)2 2π (4)(3) 32π 24π3 mm 56π 175.8The surface area is about175.8 square millimeters.Exercises 8 –10264Chapter 64 mm1. A cylinder has a radius of 2 meters and a height of 5 meters.Find the surface area of the cylinder. Round your answer tothe nearest tenth.Surface Areas of Solids
EnglishSpanishEXAMPLE2Finding Surface AreaHow much paper is used for the label onthe can of peas?1 in.Find the lateral surface area of the cylinder.2 in.Do not include the area ofthe bases in the formula.S 2π rh 2π (1)(2)Substitute. 4 π 12.56Multiply.About 12.56 square inches of paper is used for the label.EXAMPLE2 in.3Real-Life ApplicationYou earn 0.01 for recycling the can in Example 2. How much can youexpect to earn for recycling the tomato can? Assume that the recyclevalue is proportional to the surface area.Find the surface area of each can.TomatoesPeasS 2π r 2π rhS 2π r 2 2π rh25.5 in. 2π (2)2 2π (2)(5.5) 2π (1)2 2π (1)(2) 8 π 22π 2π 4 π 30π 6πUse a proportion to find the recycle value x of the tomato can.30 π in.2x6π in.2 0.01surface area— — 5 0.01 x30π 0.01 x 6 π0.05 xrecycle valueUse Cross Products Property.Divide each side by 6π.Simplify.You can expect to earn 0.05 for recycling the tomato can.Exercises 11–132. WHAT IF? In Example 3, the height of the can of peasis doubled.a. Does the amount of paper used in the label double?b. Does the recycle value double? Explain.Section 6.3Surface Areas of Cylinders265
EnglishSpanishExercises6.3Help with Homework1. CRITICAL THINKING Which part of the formula S 2π r 2 2π r h representsthe lateral surface area of a cylinder?2. CRITICAL THINKING Given the height and the circumference of the baseof a cylinder, describe how to find the surface area of the entire cylinder.6 cmFind the indicated area of the cylinder.3. Area of a base3 cm4. Surface area6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Make a net for the cylinder. Then find the surface area of the cylinder. Round youranswer to the nearest tenth.5.6.3 ft7.4m2 ft7 ft1m5 ftFind the surface area of the cylinder. Round your answer to the nearest tenth.18.5 mm9.10.6 ft12 cm2 mm6 cm7 ftFind the lateral surface area of the cylinder. Round your answer to the nearest tenth.2 11.12.10 ft6 ft13.9 in.14 m2m4 in.50 ft14. TANKER The truck’s tankis a stainless steel cylinder.Find the surface area ofthe tank.radius â 4 ft266Chapter 6Surface Areas of Solids
EnglishSpanish15. ERROR ANALYSIS Describe andcorrect the error in finding thesurface area of the cylinder.16 in. 6 ft11 ftS 2𝛑 rh 2𝛑 (6)(11) 132𝛑 ft216. OTTOMAN What percent of the surface area of theottoman is green (not including the bottom)?6 in.17. REASONING You make two cylinders using 8.5-inch by 11-inchpieces of paper. One has a height of 8.5 inches and the otherhas a height of 11 inches. Without calculating, compare thesurface areas of the cylinders.8 in.18. INSTRUMENT A ganza is a percussioninstrument used in samba music.a. Find the surface area of each of the twolabeled ganzas.b. The weight of the smaller ganza is 1.1 pounds.Assume that the surface area is proportional tothe weight. What is the weight of the larger ganza?19. BRIE CHEESE The cut wedge represents one-eighthof the cheese.10cm23.5 cm5.5 cm20.54.cma. Find the surface area of thecheese before it is cut.3 in.b. Find the surface area ofthe remaining cheese afterthe wedge is removed. Didthe surface area increase,decrease, or remain the same?1 in.The lateral surface area of a cylinder is184 square centimeters. The radius is 9 centimeters. What is thesurface area of the cylinder? Explain how you found your answer.Evaluate the expression. SKILLS REVIEW HANDBOOK1221. —(26)(9)1222. —(8.24)(3) 8.241223. —(18.84)(3) 28.2624. MULTIPLE CHOICE A store pays 15 for a basketball. The percent of markup is30%. What is the selling price?SECTION 4.3A 10.50 B 19.50 C 30 Section 6.3D 34.50 Surface Areas of Cylinders267
of a cylinder, describe how to fi nd the surface area of the entire cylinder. Find the indicated area of the cylinder. 3. Area of a base 4. Surface area Make a net for the cylinder. Then fi nd the surface area of the cylinder. Round your answer to the nearest tenth. 5. 3 ft 2 ft 6. 1 m 4 m 7. 7 ft 5 ft Find the surface area of the cylinder.
Section 6.2 Surface Areas of Prisms 259 Surface Area of a Prism The surface area S of a prism is the sum of the areas of the bases and the lateral faces. S areas of bases areas of lateral faces EXAMPLE 2 Finding the Surface Area of a Triangular Prism Find the surface area of the prism. Draw a net. 4 m 3 m 5 m 4 m 6 m 3 m Add the areas of the bases and the lateral faces.
Aug 26, 2009 · EXAMPLE 2 Finding the Surface Area of a Triangular Prism Find the surface area of the prism. Draw a net. 4 m 3 m 5 m 4 m 6 m 3 m Add the areas of the bases and the lateral faces. S areas of bases areas of lateral faces 6 6 18 30 24 84 The surface area is 84 square meters. Find the surface are
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Importance of Surface Finish Title. Lotus Leaf . Surface Topography of Lotus Leaf. Surface Integrity Surface Topography Surface Roughness Profile Surface Metallurgy Sub surface material characteristics . - Peak to Valley measure L m R R q R a T. Amplitude Based Parameters Limitations
variations in surface characteristics, and it is important for engineers to understand the technology of surface. The most commonly used measure of surface texture is surface roughness. Withrespected to figure 1.2, surface roughness can be defined as the average of vertical deviations from nominal surface over a specified surface length.
ect. For concrete, SSPC-SP 13/ NACE No. 6, Surface Preparation of Concrete, defines surface preparation as “[t]he method or combination of methods used to clean a concrete surface, remove loose and weak materials and contaminants from the surface, repair the surface, and roughen the surface
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surface roughness can be seen in Figures 3 through 5 as examples of the observations. Fig. 4. Example of a surface with relatively average surface roughness. (0.335 μm) Fig. 3. Example of a surface with relatively low surface roughness. (0.141 μm) Table 1. 3D Surface roughness parameters Parameters Name Definition Comments Sa Average Roughness
