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Splash Screen. Five-Minute Check (over Lesson 1–6) Then/Now New Vocabulary Key Concept: Types of Solids Example 1: Identify Solids Key Concept: Platonic Solids Key Concept: Surface Area and Volume Example 2: Find Surface Area and Volume

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lesson menu

Five-Minute Check (over Lesson 1–6)

Then/Now

New Vocabulary

Key Concept: Types of Solids

Example 1: Identify Solids

Key Concept: Platonic Solids

Key Concept: Surface Area and Volume

Example 2: Find Surface Area and Volume

Example 3: Real-World Example: Surface Area and Volume

Lesson Menu
5 minute check 1
A

B

C

D

Name polygon A by its number of sides.

A. pentagon

B. heptagon

C. octagon

D. decagon

5-Minute Check 1
5 minute check 2
A

B

C

D

Name polygon B by its number of sides.

A. pentagon

B. hexagon

C. heptagon

D. octagon

5-Minute Check 2
5 minute check 3
A

B

C

D

Find the perimeter of polygon A.

A. 25 cm

B. 35 cm

C. 40 cm

D. 45 cm

5-Minute Check 3
5 minute check 4
A

B

C

D

Find the perimeter of polygon B.

A. 40 in.

B. 42 in.

C. 45 in.

D. 85 in.

5-Minute Check 4
5 minute check 5
A

B

C

D

Classify the polygons as regular or irregular.

A. polygon A: regularpolygon B: regular

B. polygon A: regularpolygon B: irregular

C. polygon A: irregularpolygon B: regular

D. polygon A: irregularpolygon B: irregular

5-Minute Check 5
5 minute check 6
A

B

C

D

A regular hexagon has a perimeter of 90 meters. What is the length of one side of the hexagon?

A. 18 meters

B. 10 meters

C. 11.25 meters

D. 15 meters

5-Minute Check 6
then now

You identified and named two-dimensional figures. (Lesson 1–6)

  • Identify and name three-dimensional figures.
  • Find surface area and volume.
Then/Now
vocabulary

cylinder

  • cone
  • sphere
  • regular polyhedron
  • Platonic solid
  • surface area
  • volume
  • polyhedron
  • face
  • edge
  • vertex
  • prism
  • base
  • pyramid
Vocabulary
example 1

Identify Solids

A.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1
example 11

Answer: rectangular prism;Bases: rectangles EFHG, ABDCFaces: rectangles FBDH, EACG, GCDH,EFAB, EFGH, ABCD

Vertices: A, B, C, D, E, F, G, H

Identify Solids

The solid is formed by polygonal faces, so it is a polyhedron. The bases are rectangles. This solid is a rectangular prism.

Example 1
example 12

Identify Solids

B.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1
example 13

Answer: hexagonal prism;Bases: hexagon EFGHIJ and hexagon KLMNOP

Faces: rectangles EFLK, FGML, GHMN, HNOI, IOPJ, JPKE

Vertices:E, F, G, H, I, J, K, L, M, N, O, P

Identify Solids

The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism.

Example 1
example 14

Identify Solids

C.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1
example 15

Identify Solids

The solid has a curved surface, so it is not a polyhedron. The base is a circle and there is one vertex. So, it is a cone.

Answer:Base: circle TVertex:Wno faces or edges

Example 1
example 16
A

B

C

D

A. Identify the solid.

A. triangular pyramid

B. pentagonal prism

C. rectangular prism

D. square pyramid

Example 1
example 17
A

B

C

D

B. Identify the solid.

A. cone

B. cylinder

C. pyramid

D. polyhedron

Example 1
example 18
A

B

C

D

C. Identify the solid.

A. triangular prism

B. triangular pyramid

C. rectangular pyramid

D. cone

Example 1
example 2

π

π

.

Use a calculator.

Find Surface Area and Volume

Find the surface area and volume of the cone.

Example 2
example 21

Volume of a cone

r = 3, h = 4

Simplify.

Use a calculator.

Find Surface Area and Volume

Answer: The cone has a surface area of about 75.4 cm2 and a volume of about 37.7 cm3.

Example 2
example 22
A

B

C

D

Find the surface area and volume of the triangular prism.

A. surface area = 288 ft2volume = 336 ft3

B. surface area = 336 ft2volume = 288 ft3

C. surface area = 26 ft2volume = 60 ft3

D. surface area = 488 ft2volume = 122 ft3

Example 2
example 3

A. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters andarchitectural plans. The diameter of the base is inches, and the height is feet. Find theamount of cardboard Mike needs to make the tube.

Surface Area and Volume

The amount of material used to make the tube would be equivalent to the surface area of the cylinder.

Example 3
example 31

399.1

Use a calculator.

Surface Area and Volume

Surface area of a cylinder

r = 1.875 in., h = 32 in.

Answer:Mike needs about 399.1 square inches ofcardboard to make the tube.

Example 3
example 32

B. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters andarchitectural plans. The diameter of the base is inches, and the height is feet. Find thevolume of the tube.

r = 1.875 in., h = 32 in.

353.4

Use a calculator.

Surface Area and Volume

Volume of a cylinder

Example 3
example 33

Surface Area and Volume

Answer:The volume of the tube is about 353.4 cubic inches.

Example 3
example 34
A

B

C

D

A. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the surface area of the box.

A. surface area = 2520 in2

B. surface area = 18 in2

C. surface area = 180 in2

D. surface area = 1144 in2

Example 3
example 35
A

B

C

D

B. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the volume of the box.

A. volume = 1144 in3

B. volume = 14 in3

C. volume = 2520 in3

D. volume = 3600 in3

Example 3