Transcript Glencoe Geometry - Burlington County Institute of Technology

Five-Minute Check (over Lesson 1–6)
CCSS
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
Over Lesson 1–6
Name polygon A by its
number of sides.
A. pentagon
B. heptagon
C. octagon
D. decagon
Over Lesson 1–6
Name polygon B by its
number of sides.
A. pentagon
B. hexagon
C. heptagon
D. octagon
Over Lesson 1–6
Find the perimeter of polygon A.
A. 25 cm
B. 35 cm
C. 40 cm
D. 45 cm
Over Lesson 1–6
Find the perimeter of polygon B.
A. 40 in.
B. 42 in.
C. 45 in.
D. 85 in.
Over Lesson 1–6
Classify the polygons
as regular or irregular.
A. polygon A: regular
polygon B: regular
B. polygon A: regular
polygon B: irregular
C. polygon A: irregular
polygon B: regular
D. polygon A: irregular
polygon B: irregular
Over Lesson 1–6
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
Content Standards
G.GMD.3 Use volume formulas for cylinders,
pyramids, cones, and spheres to solve
problems.
Mathematical Practices
2 Reason abstractly and quantitatively.
6 Attend to precision.
You identified and named two-dimensional
figures.
• Identify and name three-dimensional figures.
• Find surface area and volume.
• polyhedron
• cylinder
• face
• cone
• edge
• sphere
• vertex
• regular polyhedron
• prism
• Platonic solid
• base
• surface area
• pyramid
• volume
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.
Identify Solids
The solid is formed by polygonal faces, so it is a
polyhedron. The bases are rectangles. This solid is a
rectangular prism.
Answer: rectangular prism;
Bases: rectangles EFHG, ABDC
Faces: rectangles FBDH, EACG, GCDH,
EFBA, EFHG, ABDC
Vertices: A, B, C, D, E, F, G, H
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.
Identify Solids
The solid is formed by polygonal faces, so it is a
polyhedron. The bases are hexagons. This solid is a
hexagonal prism.
Answer: hexagonal prism;
Bases: hexagon EFGHIJ and hexagon
KLMNOP
Faces: rectangles EFLK, FGML, GHNM,
HNOI, IOPJ, JPKE; hexagons EFGHIJ
and KLMNOP
Vertices: E, F, G, H, I, J, K, L, M, N, O, P
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.
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 T
Vertex: W
no faces or edges
A. Identify the solid.
A. triangular pyramid
B. pentagonal prism
C. rectangular prism
D. square pyramid
B. Identify the solid.
A. cone
B. cylinder
C. pyramid
D. polyhedron
C. Identify the solid.
A. triangular prism
B. triangular pyramid
C. rectangular pyramid
D. cone
Find Surface Area and Volume
Find the surface area and volume of
the cone.
π
π
.
Use a calculator.
Find Surface Area and Volume
Volume of a cone
r = 3, h = 4
Simplify.
Use a calculator.
Answer: The cone has a surface area of about
75.4 cm2 and a volume of about 37.7 cm3.
Find the surface area and
volume of the triangular prism.
A. surface area = 288 ft2
volume = 336 ft3
B. surface area = 336 ft2
volume = 288 ft3
C. surface area = 26 ft2
volume = 60 ft3
D. surface area = 488 ft2
volume = 122 ft3
Surface Area and Volume
A. CONTAINERS Mike is creating a mailing tube
which can be used to mail posters and
architectural plans. The diameter of the base is
inches, and the height is
feet. Find the
amount of cardboard Mike needs to make the tube.
The amount of material used to make the tube would
be equivalent to the surface area of the cylinder.
Surface Area and Volume
Surface area of
a cylinder
r = 1.875 in., h = 32 in.
399.1
Use a calculator.
Answer: Mike needs about 399.1 square inches of
cardboard to make the tube.
Surface Area and Volume
B. CONTAINERS Mike is creating a mailing tube
which can be used to mail posters and
architectural plans. The diameter of the base is
inches, and the height is
feet. Find the
volume of the tube.
Volume of a cylinder
r = 1.875 in., h = 32 in.
353.4
Use a calculator.
Surface Area and Volume
Answer: The volume of the tube is about
353.4 cubic inches.
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
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