lesson 8.2b lateral and surface area of pyramids and cones standards: m.3.g.2 m.3.g.3

Lesson 8.2B Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

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Lesson 8.2BLesson 8.2BLateral and Surface Area of

Pyramids and ConesStandards: M.3.G.2

M.3.G.3

ReviewReview

Surface Area:The sum of the areas of the faces

of a polyhedron

Lateral Area:The sum of the areas of the faces

of a polyhedron except for the base

Page 3: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Lateral Area - PyramidsLateral Area - Pyramids

Lateral Area = ½ P l

P: Perimeter of the base

l: slant height

Page 4: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

ExampleExample

Find the lateral area of the right square pyramid. Round your answer to the nearest whole number:

18'

24'

Page 5: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Surface Area - PyramidsSurface Area - Pyramids

Surface Area = LA + B

LA: Lateral Area

B: Area of the Base

Page 6: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

ExampleExample

Find the surface area of the right square pyramid. Round your answer to the nearest whole number:

10'

12'

Page 7: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Now You Try…Now You Try…

Find the lateral area and the surface area of the regular triangular pyramid. Round your answer to the nearest whole number:

13”

10”

Page 8: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Lateral Area - ConesLateral Area - Cones

Lateral Area = π r l

r: radius of the base

l: slant height

Page 9: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

ExampleExample

Find the lateral area of the cone. Round your answer to the nearest whole number.

12"

Page 10: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Surface Area - ConesSurface Area - Cones

Surface Area = π r l + π r2

r: radius of the base

l : slant height

Page 11: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

ExampleExample

Find the surface area of the cone. Round your answer to the nearest whole number.

15"

Page 12: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Now You Try…Now You Try…

Find the lateral area and the surface area of the cone. Round your answer to the nearest whole number.

11"

31"

Page 13: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Real Life Application Real Life Application ProblemsProblemsExample:The framework for a decorative

trellis to support a grapevine is in the shape of a square pyramid. If the height is 6 meters and the width of the base is 2 meters, what amount of netting is needed to protect the grapes from the birds? Round your answer to the nearest whole number.

Page 14: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

ExampleExampleThe framework for a decorative trellis to support a

grapevine is in the shape of a square pyramid. If the height is 6 meters and the width of the base is 2 meters, what amount of netting is needed to protect the grapes from the birds? Round your answer to the nearest whole number. 6 m

2 m

Page 15: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Now You Try…Now You Try…

A toy company plans to market a square pyramid-shaped space station component for its line of Galaxy Generation figures. The space station will need to be coated all over the outside with a reflective paint. How many square inches will need to be painted on each item? Round your answer to the nearest whole number.

Page 16: Lesson 8.2B Lateral and Surface Area of Pyramids and Cones Standards: M.3.G.2 M.3.G.3

Now You Try…Now You Try…A toy company plans to market a square pyramid-

shaped space station component for its line of Galaxy Generation figures. The space station will need to be coated all over the outside with a reflective paint. How many square inches will need to be painted on each item? Round your answer to the nearest whole number.

8”

16”

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