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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 Lesson Menu

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

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

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. 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. 5-Minute Check 2

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

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

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

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

Mathematical Practices 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. CCSS

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

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

Concept

Find the lateral area of the regular hexagonal prism. 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. Lateral area of a prism P = 30, h = 12 Multiply. Answer: Example 1

Find the lateral area of the regular hexagonal prism. 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. Lateral area of a prism P = 30, h = 12 Multiply. Answer: The lateral area is 360 square centimeters. Example 1

Find the lateral area of the regular octagonal prism. A. 162 cm2 B. 216 cm2 C. 324 cm2 D. 432 cm2 Example 1

Find the lateral area of the regular octagonal prism. A. 162 cm2 B. 216 cm2 C. 324 cm2 D. 432 cm2 Example 1

Concept

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

Surface area of a prism L = Ph Substitution Simplify. Answer: Example 2

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

Find the surface area of the triangular prism. A. 320 units2 B. 512 units2 C. 368 units2 D. 416 units2 Example 2

Find the surface area of the triangular prism. A. 320 units2 B. 512 units2 C. 368 units2 D. 416 units2 Example 2

Concept

L = 2rh Lateral area of a cylinder 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rh Lateral area of a cylinder = 2(14)(18) Replace r with 14 and h with 18. ≈ 1583.4 Use a calculator. Example 3

S = 2rh + 2r2 Surface area of a cylinder Lateral Area and Surface Area of a Cylinder S = 2rh + 2r2 Surface area of a cylinder ≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4 and r with 14. ≈ 2814.9 Use a calculator. Answer: Example 3

S = 2rh + 2r2 Surface area of a cylinder Lateral Area and Surface Area of a Cylinder S = 2rh + 2r2 Surface area of a cylinder ≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4 and r with 14. ≈ 2814.9 Use a calculator. Answer: The lateral area is about 1583.4 square feet and the surface area is about 2814.9 square feet. Example 3

A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 B. lateral area ≈ 1508 ft2 and surface area ≈ 1206.4 ft2 C. lateral area ≈ 754 ft2 and surface area ≈ 2412.7 ft2 D. lateral area ≈ 754 ft2 and surface area ≈ 1206.4.7 ft2 Example 3

A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 B. lateral area ≈ 1508 ft2 and surface area ≈ 1206.4 ft2 C. lateral area ≈ 754 ft2 and surface area ≈ 2412.7 ft2 D. lateral area ≈ 754 ft2 and surface area ≈ 1206.4.7 ft2 Example 3

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

Find Missing Dimensions Answer: Example 4

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

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

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

End of the Lesson