splash screen. lesson menu five-minute check (over lesson 12–1) ccss then/now new vocabulary key...
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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
Over Lesson 12–1
Use isometric dot paper to sketch a cube 2 units on each edge.
A. B.
C. D.
Over Lesson 12–1
Use isometric dot paper to sketch a cube 2 units on each edge.
A. B.
C. D.
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.
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.
Over Lesson 12–1
Use isometric dot paper and the orthographic drawing to sketch a solid.
A. B.
C. D.
Over Lesson 12–1
Use isometric dot paper and the orthographic drawing to sketch a solid.
A. B.
C. D.
Over Lesson 12–1
A. triangle
B. rectangle
C. trapezoid
D. rhombus
Describe the cross section of a rectangular solid sliced on the diagonal.
Over Lesson 12–1
A. triangle
B. rectangle
C. trapezoid
D. rhombus
Describe the cross section of a rectangular solid sliced on the diagonal.
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.
You found areas of polygons.
• Find lateral areas and surface areas of prisms.
• Find lateral areas and surface areas of cylinders.
• lateral face
• lateral edge
• base edge
• altitude
• height
• lateral area
• axis
• composite solid
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.
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.
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Find the lateral area of the regular octagonal prism.
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Find the lateral area of the regular octagonal prism.
Surface Area of a Prism
Find the surface area of the rectangular prism.
Surface Area of a Prism
Answer:
Surface area of a prism
L = Ph
Substitution
Simplify.
Surface Area of a Prism
Answer: The surface area is 360 square centimeters.
Surface area of a prism
L = Ph
Substitution
Simplify.
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Find the surface area of the triangular prism.
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Find the surface area of the triangular prism.
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.
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.
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.
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.
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.
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.
Find Missing Dimensions
Answer:
Find Missing Dimensions
Answer: The radius of the soup can is about 2.5 inches.
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.
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.