Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–1) CCSS Then/Now New Vocabulary Key...
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Transcript of Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–1) CCSS Then/Now New Vocabulary Key...
![Page 1: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/1.jpg)
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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
![Page 3: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/3.jpg)
Over Lesson 12–1
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
Use isometric dot paper to sketch a cube 2 units on each edge.
A. B.
C. D.
![Page 5: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/5.jpg)
Over Lesson 12–1
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.
![Page 6: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/6.jpg)
Over Lesson 12–1
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.
![Page 7: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/7.jpg)
Over Lesson 12–1
Use isometric dot paper and the orthographic drawing to sketch a solid.
A. B.
C. D.
![Page 8: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/8.jpg)
Over Lesson 12–1
Use isometric dot paper and the orthographic drawing to sketch a solid.
A. B.
C. D.
![Page 9: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/9.jpg)
Over Lesson 12–1
A. triangle
B. rectangle
C. trapezoid
D. rhombus
Describe the cross section of a rectangular solid sliced on the diagonal.
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Over Lesson 12–1
A. triangle
B. rectangle
C. trapezoid
D. rhombus
Describe the cross section of a rectangular solid sliced on the diagonal.
![Page 11: Splash Screen. 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.](https://reader036.fdocuments.net/reader036/viewer/2022070323/56649da75503460f94a92ec8/html5/thumbnails/11.jpg)
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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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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• lateral face
• lateral edge
• base edge
• altitude
• height
• lateral area
• axis
• composite solid
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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:
Lateral area of a prism
P = 30, h = 12
Multiply.
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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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A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Find the lateral area of the regular octagonal prism.
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A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Find the lateral area of the regular octagonal prism.
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Surface Area of a Prism
Find the surface area of the rectangular prism.
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Surface Area of a Prism
Answer:
Surface area of a prism
L = Ph
Substitution
Simplify.
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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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A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Find the surface area of the triangular prism.
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A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Find the surface area of the triangular prism.
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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 = 2rh Lateral area of a cylinder
= 2(14)(18) Replace r with 14 and h with 18.
≈ 1583.4 Use a calculator.
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Lateral Area and Surface Area of a Cylinder
Answer:
S = 2rh + 2r2 Surface area of a cylinder
≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4
and r with 14.
≈ 2814.9 Use a calculator.
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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 = 2rh + 2r2 Surface area of a cylinder
≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4
and r with 14.
≈ 2814.9 Use a calculator.
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A. lateral area ≈ 1508 ft2 andsurface area ≈ 2412.7 ft2
B. lateral area ≈ 1508 ft2 andsurface area ≈ 1206.4 ft2
C. lateral area ≈ 754 ft2 andsurface area ≈ 2412.7 ft2
D. lateral area ≈ 754 ft2 andsurface area ≈ 1206.4.7 ft2
Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.
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A. lateral area ≈ 1508 ft2 andsurface area ≈ 2412.7 ft2
B. lateral area ≈ 1508 ft2 andsurface area ≈ 1206.4 ft2
C. lateral area ≈ 754 ft2 andsurface area ≈ 2412.7 ft2
D. lateral area ≈ 754 ft2 andsurface area ≈ 1206.4.7 ft2
Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.
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Find Missing Dimensions
MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?
L = 2rh Lateral area of a cylinder
125.6 = 2r(8) Replace L with 15.7 ● 8 and h with 8.
125.6 = 16r Simplify.
2.5 ≈ r Divide each side by 16.
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Find Missing Dimensions
Answer:
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Find Missing Dimensions
Answer: The radius of the soup can is about 2.5 inches.
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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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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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