9.1 Surface Areas Of Prisms
9.1Surface Areas of PrismsHow can you find the surface area of a prism?1ACTIVITY: Surface Area of a Rectangular PrismWork with a partner. Copy the net for a rectangular prism. Label each sideas h, w, or ℓ. Then use your drawing to write a formula for the surface areaof a rectangular prism.hw2ACTIVITY: Surface Area of a Triangular PrismWork with a partner.a. Find the surface area of the solid shown by the net. Copy the net, cut it out,and fold it to form a solid. Identify the solid.43COMMONCOREGeometryIn this lesson, you will use two-dimensionalnets to representthree-dimensional solids. find surface areas ofrectangular andtriangular prisms. solve real-life problems.Learning Standard7.G.6345334b. Which of the surfaces of the solid are bases? Why?354Chapter 9Surface Area and Volume
3MathPracticeConstructArgumentsWhat method didyou use to find thesurface area of therectangular prism?Explain.ACTIVITY: Forming Rectangular Prismsi msWork with a partner. Use 24 one-inch cubes to forma rectangular prism that hasthe given dimensions. Draw each prism. Find the surface area of each prism.isma. 4 3 2DrawingSurface Areain.2b. 1 1 24c. 1 2 12d. 1 3 8e. 1 4 6f. 2 2 6g. 2 4 34. Use your formula from Activity 1 to verify your results in Activity 3.5. IN YOUR OWN WORDS How can you find the surface area of a prism?6. REASONING When comparing ice blocks with the same volume, the icewith the greater surface area will melt faster. Which will melt faster, thebigger block or the three smaller blocks? Explain your reasoning.3 ft1 ft1 ft1 ft1 ft1 ftUse what you learned about the surface areas of rectangular prismsto complete Exercises 4 – 6 on page 359.Section 9.1Surface Areas of Prisms355
Lesson9.1Lesson TutorialsKey Vocabularylateral surface area,p. 358Surface Area of a Rectangular PrismWordsThe surface area S of a rectangular prism is the sum of theareas of the bases and the lateral eralfacewbaseAlgebraS 2ℓw 2ℓh 2whAreas ofbasesEXAMPLE1Areas oflateral facesFinding the Surface Area of a Rectangular PrismFind the surface area of the prism.3 in.Draw a net.S 2ℓw 2ℓh 2wh6 in.5 in.5 in. 3 in.5 in. 2(3)(5) 2(3)(6) 2(5)(6)6 in. 30 36 605 in.3 in. 126The surface area is 126 square inches.Find the surface area of the prism.Exercises 7–91.2.4 ft5m8m3 ft2 ft356Chapter 9Surface Area and Volume8mh
Surface Area of a PrismThe surface area S of any prism is the sum of the areas of the basesand the lateral faces.S areas of bases areas of lateral facesEXAMPLE2Finding the Surface Area of a Triangular PrismFind the surface area of the prism.5mDraw a net.4m3m3m6m4m5m6m4m3mRememberArea of a Base12The area A of a trianglewith base b and heightAreas of Lateral Faces Purple lateral face: 5 6 30Blue lateral face: 4 6 24Green lateral face: 3 6 18 Red base: — 3 4 612h is A — bh.Add the areas of the bases and the lateral faces.S areas of bases areas of lateral faces 6 6 18 30 24There are two identicalbases. Count the area twice. 84The surface area is 84 square meters.Find the surface area of the prism.Exercises 10–123.5m12 m4.4 cm3m5 cm13 m4 cm3 cmSection 9.1Surface Areas of Prisms357
RememberA cube has 6 congruentsquare faces.EXAMPLEWhen all the edges of a rectangular prism have thesame length s, the rectangular prism is a cube. Theformula for the surface area of a cube isS 6s2.3sFormula for surface area of a cubessFinding the Surface Area of a CubeFind the surface area of the cube.12 mS 6s 212 m12 mWrite formula for surface area of a cube. 6(12)2Substitute 12 for s. 864Simplify.The surface area of the cube is 864 square meters.The lateral surface area of a prism is the sum of the areas of thelateral faces.EXAMPLE4Real-Life ApplicationThe outsides of purple traps are coated with glueto catch emerald ash borers. You make your owntrap in the shape of a rectangular prism with anopen top and bottom. What is the surface areathat you need to coat with glue?20 in.Find the lateral surface area.S 2ℓh 2whDo not include the areas ofthe bases in the formula. 2(12)(20) 2(10)(20)Substitute. 480 400Multiply.y. 880Add.12 in.10 in.So, you need to coat 880 square inches with glue.Exercises 13–155. Which prism has the greatersurface area?6. WHAT IF? In Example 4, boththe length and the width ofyour trap are 12 inches. Whatis the surface area that youneed to coat with glue?358Chapter 9Surface Area and Volume9 cm7 cm9 cm15 cm9 cm5 cm
Exercises9.1Help with Homework1. VOCABULARY Describe two ways to find the surface area ofa rectangular prism.2. WRITING Compare and contrast a rectangular prism to a cube.3. DIFFERENT WORDS, SAME QUESTION Which is different?Find “both” answers.Find the surfacearea of the prism.Find the area of thebases of the prism.Find the area of thenet of the prism.Find the sum of the areas of the basesand the lateral faces of the prism.7 in.4 in.3 in.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Use one-inch cubes to form a rectangular prism that has the given dimensions.Then find the surface area of the prism.4. 1 2 35. 3 4 16. 2 3 2Find the surface area of the prism.17.3m8.9.3 yd7 mm16 m5 yd4 mm6m5 mm12 10.17 ft11.5m1yd512.13.5 in.9 in.5m8 ft4m20 ft7m6m9 in.15 ft3 13.14.15.7 yd2ft30.5 cm7 yd7 yd10 in.0.5 cm2ft30.5 cmSection 9.12ft3Surface Areas of Prisms359
16. ERROR ANALYSIS Describe and correctthe error in finding the surface area ofthe prism.S 2(5)(3) 2(3)(4) 2(5)(3) 30 24 30 84 in.24 in.5 in.3 in.17. GAME Find the surface area of the tin game case.10 in.10 in.8.7 in.18. WRAPPING PAPER A cube-shaped gift is11 centimeters long. What is the least amountof wrapping paper you need to wrap the gift?3 in.3 in.10 in.19. FROSTING One can of frosting covers about280 square inches. Is one can of frostingenough to frost the cake? Explain.9 in.13 in.Find the surface area of the prism.20.12 in.21.4 in.3 in.5 in.6 in.2.5 m2m5 in.4m4m22. OPEN-ENDED Draw and label a rectangular prism that hasa surface area of 158 square yards.3 in.2 in.23. LABEL A label that wraps around a box of golf balls covers75% of its lateral surface area. What is the value of x?x in.h24. BREAD Fifty percent of the surface area ofthe bread is crust. What is the height h?10 cm10 cm360Chapter 9Surface Area and Volume2 in.
Compare the dimensions of the prisms. How many times greater is thesurface area of the red prism than the surface area of the blue prism?25.26.4m6 ft4 ft9m3m2m4 ft6 ft4 ft6m6 ft12 m27. STRUCTURE You are painting the prize pedestals shown (including the bottoms).You need 0.5 pint of paint to paint the red pedestal.a. The side lengths of the green pedestal are one-half the sidelengths of the red pedestal. How much paint do youneed to paint the green pedestal?eb. The side lengths of the blue pedestal are triplethe side lengths of the green pedestal. Howmuch paint do you need to paint theblue pedestal?244 iin.c. Compare the ratio of paint amountsto the ratio of side lengths for thegreen and red pedestals. Repeat forthe green and blue pedestals. Whatdo you notice?28.16 in.16 in.A keychain-sized puzzle cube is made up of smallcubes. Each small cube has a surface area of 1.5 square inches.a. What is the side length of each small cube?b. What is the surface area of the entire puzzle cube?Find the area of the triangle (Skills Review Handbook)29.30.31.8 ft9m16 ft7 ft12 m20 ft32. MULTIPLE CHOICE What is the circumference of the basketball?Use 3.14 for π. (Section 8.1)A 14.13 in. B28.26 in. C56.52 in. D254.34 in. Section 9.1MSCA7PE 0901.indd 3619 in.Surface Areas of Prisms3614/16/13 2:24:08 PM
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
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.
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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
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