Transcript Glencoe Geometry - Dolfanescobar's Weblog

Five-Minute Check (over Lesson 12–1)
NGSSS
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.
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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.
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Over Lesson 12–1
Use isometric dot paper
and the orthographic
drawing to sketch a solid.
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Over Lesson 12–1
Describe the cross section of a rectangular solid
sliced on the diagonal.
A. triangle
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D. rhombus
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C. trapezoid
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B. rectangle
MA.912.G.7.5 Explain and use formulas for
lateral area, surface area, and volume of
solids.
MA.912.G.7.7 Determine how changes in
dimensions affect the surface area and
volume of common geometric solids.
Also MA.912.G.7.2.
You found areas of polygons. (Lesson 11–2)
• 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.
Lateral area of a prism
P = 30, h = 12
Multiply.
Answer: The lateral area is 360 square centimeters.
Find the lateral area of the regular octagonal prism.
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
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Surface Area of a Prism
Find the surface area of the rectangular prism.
Surface Area of a Prism
Surface area of a prism
L = Ph
Substitution
Simplify.
Answer: The surface area is 360 square centimeters.
Find the surface area of the triangular prism.
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
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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 = 2rh
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
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.
Find the lateral area and the surface
area of the cylinder. Round to the
nearest tenth.
C. lateral area ≈ 754 ft2 and
surface area ≈ 2412.7 ft2
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D. lateral area ≈ 754 ft2 and
surface area ≈ 1206.4.7 ft2
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B. lateral area ≈ 1508 ft2 and
surface area ≈ 1206.4 ft2
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A. lateral area ≈ 1508 ft2 and
surface area ≈ 2412.7 ft2
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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 = 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.
Find Missing Dimensions
Answer: The radius of the soup can is about
2.5 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
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D. 24 inches
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C. 18 inches
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B. 16 inches