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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 MenuA

B

C

D

Name polygon A by its number of sides.

A. pentagon

B. heptagon

C. octagon

D. decagon

5-Minute Check 1A

B

C

D

Name polygon B by its number of sides.

A. pentagon

B. hexagon

C. heptagon

D. octagon

5-Minute Check 2A

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 5A

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

- Identify and name three-dimensional figures.

- Find surface area and volume.

- cone
- sphere
- regular polyhedron
- Platonic solid
- surface area
- volume

- polyhedron

- face
- edge
- vertex
- prism
- base
- pyramid

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 1Answer: 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 1B.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1Answer: 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 1C.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1The 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 1r = 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 2A. 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 3B. 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 3A

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
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