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Lesson Menu Five-Minute Check (over Lesson 12–1) CCSS Then/Now New Vocabulary Key Concept: Lateral Area of a Prism Example 1:Lateral Area of a Prism Key Concept: Surface Area of a Prism Example 2:Surface Area of a Prism Key Concept: Areas of a Cylinder Example 3:Lateral Area and Surface Area of a Cylinder Example 4:Real-World Example: Find Missing Dimensions

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Over Lesson 12–1 5-Minute Check 1 Use isometric dot paper to sketch a cube 2 units on each edge. A.B. C.D.

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Over Lesson 12–1 5-Minute Check 2 Use isometric dot paper to sketch a triangular prism 3 units high with two sides of the base that are 5 units long and 2 units long. A.B. C.D.

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Over Lesson 12–1 5-Minute Check 3 Use isometric dot paper and the orthographic drawing to sketch a solid. A.B. C.D.

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Over Lesson 12–1 5-Minute Check 4 A.triangle B.rectangle C.trapezoid D.rhombus Describe the cross section of a rectangular solid sliced on the diagonal.

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CCSS Content Standards G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 1 Make sense of problems and persevere in solving them. 6 Attend to precision.

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Then/Now You found areas of polygons. Find lateral areas and surface areas of prisms. Find lateral areas and surface areas of cylinders.

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Vocabulary lateral face lateral edge base edge altitude height lateral area axis composite solid

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Concept

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Example 1 Lateral Area of a Prism Find the lateral area of the regular hexagonal prism. The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters. Answer:The lateral area is 360 square centimeters. Lateral area of a prism P = 30, h = 12 Multiply.

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Example 1 A.162 cm 2 B.216 cm 2 C.324 cm 2 D.432 cm 2 Find the lateral area of the regular octagonal prism.

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Concept

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Example 2 Surface Area of a Prism Find the surface area of the rectangular prism.

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Example 2 Surface Area of a Prism Answer:The surface area is 360 square centimeters. Surface area of a prism L = Ph Substitution Simplify.

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Example 2 A.320 units 2 B.512 units 2 C.368 units 2 D.416 units 2 Find the surface area of the triangular prism.

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Concept

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Example 3 Lateral Area and Surface Area of a Cylinder Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. L=2 rhLateral area of a cylinder =2 (14)(18)Replace r with 14 and h with 18. ≈1583.4Use a calculator.

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Example 3 Lateral Area and Surface Area of a Cylinder Answer:The lateral area is about 1583.4 square feet and the surface area is about 2814.9 square feet. S=2 rh + 2 r 2 Surface area of a cylinder ≈1583.4 + 2 (14) 2 Replace 2 rh with 1583.4 and r with 14. ≈2814.9Use a calculator.

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Example 3 A.lateral area ≈ 1508 ft 2 and surface area ≈ 2412.7 ft 2 B.lateral area ≈ 1508 ft 2 and surface area ≈ 1206.4 ft 2 C.lateral area ≈ 754 ft 2 and surface area ≈ 2412.7 ft 2 D.lateral area ≈ 754 ft 2 and surface area ≈ 1206.4.7 ft 2 Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

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Example 4 Find Missing Dimensions MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can? L=2 rhLateral area of a cylinder 125.6=2 r(8)Replace L with 15.7 ● 8 and h with 8. 125.6=16 rSimplify. 2.5≈rDivide each side by 16 .

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Example 4 Find Missing Dimensions Answer:The radius of the soup can is about 2.5 inches.

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Example 4 A.12 inches B.16 inches C.18 inches D.24 inches Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches.

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End of the Lesson

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