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Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Identify the figure described. 1. two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles. prism. - PowerPoint PPT Presentation
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Holt CA Course 1
10-10 Surface Area
Warm UpWarm Up
Lesson PresentationLesson Presentation
California StandardsCalifornia Standards
PreviewPreview
Holt CA Course 1
10-10 Surface Area
Warm UpIdentify the figure described.
1. two parallel congruent faces, with the other faces being parallelograms
2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles
prism
pyramid
Holt CA Course 1
10-10 Surface Area
AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).Also covered: AF3.2
California Standards
1 2
Holt CA Course 1
10-10 Surface Area
Vocabulary
surface areanet
Holt CA Course 1
10-10 Surface Area
The surface area of a three-dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.
Holt CA Course 1
10-10 Surface Area
The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface.
To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base.
Helpful Hint
Holt CA Course 1
10-10 Surface AreaAdditional Example 1: Finding the Surface Area of
a Prism
Find the surface area S of the prism.
A. Method 1: Use a net.
Draw a net to help you see each face of the prism.
Use the formula A = lw to find the area of each face.
Holt CA Course 1
10-10 Surface AreaAdditional Example 1A Continued
A: A = 5 2 = 10
B: A = 12 5 = 60
C: A = 12 2 = 24
D: A = 12 5 = 60
E: A = 12 2 = 24
F: A = 5 2 = 10
S = 10 + 60 + 24 + 60 + 24 + 10 = 188Add the areas of each face.
The surface area is 188 in2.
Holt CA Course 1
10-10 Surface AreaAdditional Example 1: Finding the Surface Area of a
Prism
Find the surface area S of each prism.
B. Method 2: Use a three-dimensional drawing.
Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.
Holt CA Course 1
10-10 Surface AreaAdditional Example 1B Continued
Front: 9 7 = 63
Top: 9 5 = 45
Side: 7 5 = 35
63 2 = 126
45 2 = 90
35 2 = 70
S = 126 + 90 + 70 = 286 Add the areas of each face.
The surface area is 286 cm2.
Holt CA Course 1
10-10 Surface AreaAdditional Example 2: Finding the Surface Area of a
Pyramid
Find the surface area S of the pyramid.S = area of square + 4 (area of
triangular face)
S = 49 + 4 28
S = 49 + 112
Substitute.
S = s2 + 4 ( bh) 12__
S = 72 + 4 ( 7 8)12__
S = 161
The surface area is 161 ft2.
Holt CA Course 1
10-10 Surface AreaAdditional Example 3: Finding the Surface Area of a
Cylinder
Find the surface area S of the cylinder. Write your answer in terms of .
S = area of curved surface + (2 area of each base)
Substitute 7 for h and 4 for r.
S = (h 2r) + (2 r2)
S = (7 2 4) + (2 42)
ft
S = (7 2 4)+ (2 16) Simplify the power.
Holt CA Course 1
10-10 Surface AreaAdditional Example 3 Continued
Find the surface area S of the cylinder. Write in terms of .
S = (56 + 32)
The surface area is about 88 ft2.
Multiply.
S = 88
S = 56 + 32
Use the Distributive Property.
Holt CA Course 1
10-10 Surface AreaCheck It Out! Example 1
Find the surface area S of each prism.
B. Method 2: Use a three-dimensional drawing.
Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.
6 cm 10 cm
8 cm
topfront side
Holt CA Course 1
10-10 Surface AreaCheck It Out! Example 1B Continued
Side: 10 8 = 80
Top: 10 6 = 60
Front: 8 6 = 48
80 2 = 160
60 2 = 120
48 2 = 96
S = 160 + 120 + 96 = 376 Add the areas of each face.
The surface area is 376 cm2.
6 cm 10 cm
8 cm
topfront side
Holt CA Course 1
10-10 Surface AreaCheck It Out! Example 2
Find the surface area S of the pyramid.
S = area of square + 4 (area of triangular face)
S = 25 + 4 25
S = 25 + 100
Substitute.
S = s2 + 4 ( bh) 12__
S = 52 + 4 ( 5 10)12__
S = 125The surface area is 125 ft2.
5 ft
5 ft
10 ft
10 ft
5 ft
Holt CA Course 1
10-10 Surface AreaCheck It Out! Example 3
Find the surface area S of the cylinder. Write your answer in terms of .
S = area of lateral surface + (2 area of each base)
Substitute 9 for h and 6 for r.
S = (h 2r) + (2 r2)
S = (9 2 6) + (2 62)
6 ft
9 ft
S = (9 2 6) + (2 36) Simplify the power.
Holt CA Course 1
10-10 Surface AreaCheck It Out! Example 3 Continued
Find the surface area S of the cylinder. Write your answer in terms of .
S = (108 + 72)
S = 180
The surface area is about 180ft2.
Multiply.S = 108 + 72
Use the Distributive Property.
Holt CA Course 1
10-10 Surface AreaLesson Quiz
Find the surface area of each figure. Use 3.14 as an estimate for .
1. rectangular prism with base length 6 ft, width
5 ft, and height 7 ft
2. cylinder with radius 3 ft and height 7 ft
3. Find the surface area of the figure shown.
214 ft2
≈188.4 ft2
208 ft2
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