1. How much deeper would oceans be if sponges didn’t live there?
Geometry of Solids
How much deeper would oceans be if sponges didn’t live there?
Steven Write

2. Objectives Learn the vocabulary of polyhedrons
Learn the vocabulary of spheres, cylinders, and cones.
Discover formulas for finding the volumes of prisms and cylinders.

3. What is volume?
Volume is the measure of the amount of ________ contained in a __________.
space
solid

4. Vocabulary Term Definition ______ Polyhedron ______ Faces ______ Edges
______ Vertex
______ Tetrahedron
______ Regular Polyhedron
A) Each face is congruent to the other faces. Faces meet at each vertex in exactly the same way.
B) Solid formed by polygons that enclose a single region of space.
C) Polygonal surfaces of a polyhedron.
D) A polyhedron with four faces.
E) A segment where two faces intersect.
F) Point of intersection of three of more edges. B C E F D A

5. Vocabulary Term Definition ______ Prism ______ Altitude ______ Pyramid
______ Lateral Edges
______ Right Prism
______ Lateral Faces D
A) A Polyhedron with one base.
B) Parallelograms that connect the corresponding sides of the bases.
C) Segments where the lateral faces meet.
D) A type of polyhedron with two bases that are congruent, parallel polygons.
E) Any perpendicular segment from one base to the plane of the other base.
F) A prism whose lateral faces are rectangles. E A C F B

6. Vocabulary Term Definition _____ Sphere _____ Cylinder
_____ Hemisphere
_____ Oblique Cylinder
_____ Great Circle
_____ Right Cone E
A) The circle that encloses the base of a hemisphere.
B) A type of solid with a curved surface where the line segment connecting the vertex to the center of the base is perpendicular to the base.
C) Cylinder that is not a right cylinder.
D) A solid with a curved surface that has 2 bases that are parallel and congruent.
E) The set of all points in space at a given distance from a given point.
F) Half a sphere and has a circular base. D F C A B

7. Label the Shape Bases Lateral Faces Lateral Edges Vertex
What is this shape?
Vertex
Lateral Edge
Bases
Hexagonal Prism
Lateral Face

8. Label the Shape Vertex Altitude Base Radius What is this shape?
Oblique Cone
Base
Radius

9. Volume of Prisms and Cylinders
Investigation: The Volume Formula for Prisms and Cylinder
P. 514
At each table there is a different right rectangular prism. You have 3 minutes to find the volume of the shape on your table, then we will switch tables. We will do this until each group has gone to each table.

10. Volume Chart
Use this table to organize the information you collect as you move from table to table.
Shape
Length
Width
Height
Total Volume
Table 2
Table 3
Table 4
Table 5
Table 6
Conjecture:
If B is the area of the base of a right rectangular prism and H is the height of the solid, then the formula for the volume is V = ______.
Volume = (Length * Width) * Height
Volume = (Area of Base) * Height
Volume = BH BH

11. Volume of Prisms and Cylinders
Now continue the investigation with your groups to discover the volume formula for a right prism or cylinder.
Conjecture:
If B is the area of the base of a right prism (or cylinder) and H is the height of the solid, then the formula for the volume is V = _____.
The volume of an oblique prism (or cylinder) is the same as the volume of a right prism (or cylinder) that has the same __________ and the same ______. BH
base area
height

12. Prism-Cylinder Volume Conjecture
The volume of a prism or a cylinder is the __________ multiplied by the __________.
base area
height
Cylinder:
Right Trapezoidal prism:
Cube:
V = r2(H)
V = (½ * (b1+b2)h)(H)
V = (l * w) H

13. Exit Activity
Table 2
Table 3
Table 4
Table 5
Table 6
Class
Triangular Prism
Rectangular Prism
Pentagonal Prism
Hexagonal Prism
Octagonal Prism
N-gonal Prism
Lateral Faces
Total Faces
Edges
Vertices
Volume Formula 3 4 5 6 8 n 5 6 7 8 10
n+2 9 12 15 18 24 3n 6 8 10 12 16 2n
(½ * b * h)H
(l*w)H
(½*a*s*5 )H
(½*a*s*6 )H
(½*a*s*8 )H
(½*P*a )H