Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key...
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Transcript of Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key...
![Page 1: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/1.jpg)
![Page 2: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/2.jpg)
Five-Minute Check (over Lesson 12–4)
Then/Now
New Vocabulary
Key Concept: Lateral and Surface Area of Prisms
Example 1: Surface Area of Prisms
Example 2: Real-World Example: Surface Area of Prisms
![Page 3: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/3.jpg)
Over Lesson 12–4
A. 324 in3
B. 224 in3
C. 162 in3
D. 108 in3
Find the volume of the figure.
![Page 4: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/4.jpg)
Over Lesson 12–4
A. 1003.6 cm3
B. 923.6 cm3
C. 378.7 cm3
D. 126 cm3
Find the volume of the figure.
![Page 5: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/5.jpg)
Over Lesson 12–4
A. 22.4 in3
B. 20.6 in3
C. 9.42 in3
D. 7.23 in3
Find the volume of a sphere with a radius of 1.75 inches.
![Page 6: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/6.jpg)
Over Lesson 12–4
A. 1080 mm3
B. 960 mm3
C. 360 mm3
D. 280 mm3
Find the volume of a hexagonal pyramid with a base area of 120 mm2 and height of 9 mm.
![Page 7: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/7.jpg)
Over Lesson 12–4
A. 8.5 in3
B. 7.5 in3
C. 6.5 in3
D. 5.5 in3
What is the volume of a cone with a radius of 1.2 inches and a height of 5 inches?
![Page 8: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/8.jpg)
Over Lesson 12–4
A. 48 centimeters
B. 24 centimeters
C. 36 centimeters
D. 12 centimeters
A sphere and a cone have the same volume. Both have a radius of 12 centimeters. What is the approximate height of the cone?
![Page 9: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/9.jpg)
You have already found the area of two-dimensional figures. (Lesson 11–6)
• Find lateral area and surface area of prisms.
• Find surface area of real-world objects shaped like prisms.
![Page 10: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/10.jpg)
• lateral face
• lateral area
• surface area
![Page 11: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/11.jpg)
![Page 12: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/12.jpg)
Surface Area of Prisms
A. Find the lateral and surface areas of the prism.
Find the lateral area.
L = Ph
= (2ℓ + 2w)(h)
= (2 ● 34 + 2 ● 21)(4)
= 440 cm2
Answer: The lateral area is 440 square centimeters. The surface area is 1868 square centimeters.
Find the surface area.
S = L + 2B
= L + 2ℓw
= 440 + 2(34)(21)
= 1868 cm2
![Page 13: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/13.jpg)
Surface Area of Prisms
B. Find the lateral and surface areas of the prism.
L = Ph Write the formula.
= (12 + 16 + 20)(3)P is perimeter of the
triangular base. h is the height of the prism.
= 48 ● 3 or 144 m2
Simplify.
The lateral area is made up of faces that are not parallel.
![Page 14: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/14.jpg)
Surface Area of Prisms
Find the surface area.
Answer: The lateral area of the triangular prism is 144 square meters. The surface area of the triangular prism is 336 square meters.
S = L + 2BWrite the formula.
= 144 + 192 or 336 m2
Simplify.
Substitution
![Page 15: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/15.jpg)
A. Find the lateral area and the surface area of the rectangular prism.
A. lateral area, 152 in2; surface area, 292 in2
B. lateral area, 182 in2; surface area, 322 in2
C. lateral area, 304 in2; surface area, 444 in2
D. lateral area, 364 in2; surface area, 560 in2
![Page 16: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/16.jpg)
B. Find the lateral area and the surface area of the triangular prism.
A. lateral area, 19 ft2; surface area, 31 ft2
B. lateral area, 61 ft2; surface area, 96 ft2
C. lateral area, 84 ft2; surface area, 96 ft2
D. lateral area, 96 ft2; surface area, 108 ft2
![Page 17: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/17.jpg)
Surface Area of Prisms
CARPENTRY Alex is building a large storage box out of plywood. The box is a rectangular prism measuring 5 feet long, 3 feet wide, and 2 feet high.Find the number of sheets of plywood he would need to buy to build the box if 1 sheet covers 32 square feet.
Find the lateral area.
L = Ph
= (2ℓ + 2w)h
= (2 ● 5 + 2 ● 3)2
= 32 ft2
Find the surface area.
S = L + 2B
= L + 2ℓw
= 32 + 2 ● 3 ● 5
= 32 + 30 or 62 ft2
![Page 18: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/18.jpg)
Surface Area of Prisms
One sheet of plywood covers 32 ft2 and two sheets cover 2 ● 32 or 64 ft2.
32 < 62 < 64
Answer: Alex will need at least 2 sheets of plywood.
![Page 19: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/19.jpg)
A. 1 quart
B. 2 quarts
C. 3 quarts
D. 4 quarts
Jan is painting all the sides of a rectangular cabinet. The cabinet measures 3 feet long, 4 feet wide, and 5 feet tall. How much paint will she need if one quart of paint covers 50 square feet?
![Page 20: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface.](https://reader036.fdocuments.net/reader036/viewer/2022070305/551574c955034674578b5127/html5/thumbnails/20.jpg)