Vocabulary - Geometry

Page 1 Name: _________________________________ Pd.: _______ MATH NATION: Unit 14

Textbook Chapter 11: Exploring Solids

Vocabulary:

Polyhedron

• A solid 3D figure where all the faces are polygons

• Every polyhedron has faces, edges and vertices

Page 2 PRISMS VERSES PYRAMIDS

Prisms Pyramids

Bases 2 parallel bases 1 base and 1 apex (point)

Base Shape Any polygon shape Any polygon shape

Faces Rectangular Triangular

• A cube is a prism with 6 square faces

• Other prisms and pyramids are named for the shape of their bases.

Net

• A 3D figure laid out to see all the faces and bases

Cross Section

• The intersection of a plane and a solid

Page 3

HOW TO DRAW SOLIDS

Example 1:

The diagram is below is the frame of a house. Find the number of faces, edges and vertices of the solid.

Faces: ___________

Edges: ___________

Vertices: _________

Example 2:

Describe the solid that can be made from the given net.

Page 4

Example 3:

Describe each cross section.

Example 4:

Draw and label the figure that meets each description.

Rectangular prism with length 3 cm, width 2 cm and height 5 cm

Regular pentagonal prism with side length 6 in. and height 8 in.

Cylinder with radius 4 m and height 7 m

Page 5 Chapter 11 Section 6

Volume of Prisms and Cylinders

• The volume of a 3D figure is the number of non-overlapping unit cubes of a given size that will exactly fill the interior.

V = Bh B = area of the base

h = height (connecting the bases)

Volume of a Prism Volume of a Cylinder

Examples:

Page 6

Volume of a Cube Postulate

• The volume of a cube is the cube of the length of its side.

Volume Congruence Postulate

• If two polyhedra are congruent, then they have the same volume.

Volume Addition Postulate

• The volume of a solid is the sum of the volumes of all its non-overlapping parts.

3-D Puzzle: Find the volume of the puzzle piece in cubic units.

Cavalieri’s Principle

• If two solids have the same height and the same cross-sectional area at every level, then they have the

same volume.

• Cavalieri’s principle also relates to cylinders. The two stacks have the same number of CDs, so they

have the same volume.

Page 7

Finding Volume of Prisms and Cylinders

Example 1: Find the volume of the oblique cylinder to the nearest tenth. V = ______________

Example 2: Find the volume of the triangular prism to the nearest tenth. V = ______________

Example 3: Find the volume of the pentagonal prism to the nearest tenth. V = ______________

Page 8 Example 4: Find the volume of a square prism with a base side length of 5 and a height of 7 to the nearest

tenth.

V = ______________

Example 5: Find the volume of the pentagonal prism to the nearest tenth. V = ______________

Example 6:

Example 7: Find the volume of the composite object below to the nearest tenth. V = ______________


Volume of Pyramids and Cones

V = 𝟏

𝟑 Bh B = area of the base

h = height (connecting the bases)

Volume of a Pyramid Volume of a Cylinder

Obliques and Cavalieri’s Principle

Page 10 Finding the Volume of Composite Figures (WHOLE VOLUME – CUT OUT PIECE)

Example 1: Find the volume of the composite figure below to the nearest tenth. ______________

Example 2: Find the volume of the figure below to the nearest tenth. ______________


Page 11




Page 12



Example 9: Find the volume of a cone with slant height 10 ft and height 8 ft. ______________


Volume and Surface Area of Spheres

Finding and Using Volume and Surface Area of a Sphere

Example 1: Find the volume of the composite solid. ______________

Example 2:

Page 14



Example 5:

Documents

Vocabulary - Geometry