vocabulary - geometry
TRANSCRIPT
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 = ______________
Page 9 Chapter 11 Section 7
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. ______________
Example 3: Find the volume of the figure below to the nearest tenth. ______________
Page 11
Example 4: Find the volume of the figure below to the nearest tenth. ______________
Example 5: Find the volume of the figure below to the nearest tenth. ______________
Example 6: Find the volume of the figure below to the nearest tenth. ______________
Page 12
Example 7: Find the volume of the figure below to the nearest tenth. ______________
Example 8: Find the volume of the figure below to the nearest tenth. ______________
Example 9: Find the volume of a cone with slant height 10 ft and height 8 ft. ______________
Page 13 Chapter 11 Section 8
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 3: Find the volume of the figure below to the nearest tenth. ______________
Example 4: Find the volume of the figure below to the nearest tenth. ______________
Example 5: