1. Vocabulary
Volume
The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior.
OR, volume is like cross-sectional slices of area stacked on top of each other “h” times where h = height

2. Cavalieri’s principle says that if two three-dimensional figures have the same height and have the same cross-sectional area at every level, they have the same volume.
The two stacks have
the same number of
CDs, so they have
the same volume.
A right prism and an oblique prism with the same base and height have the same volume.

4. Example 1: Finding Volumes of Prisms
Find the volume of the prism. Round to the nearest tenth, if necessary.

5. Example 2: Finding Volumes of Prisms
Find the volume of the right regular hexagonal prism. Round to the nearest tenth, if necessary.

6. Example 3: Finding Volumes of Cylinders
Find the volume of the cylinder. Give your answers in terms of  and rounded to the nearest tenth.

7. Example 4: Finding Volumes of Cylinders
Find the volume of a cylinder with base area 121 cm2 and a height equal to twice the radius. Give your answer in terms of  and rounded to the nearest tenth.

8. Remember: Scale factor is the ratio of any two corresponding lengths
Remember: Scale factor is the ratio of any two corresponding lengths. Enlargement k > 1, Reduction k < 1

9. Example 5: Exploring Effects of Changing Dimensions
The radius and height of the cylinder are multiplied by .
Show the effect on the volume by writing the equations for the two volumes.

10. Example 6
The length, width, and height of the prism are doubled. Describe the effect on the volume.
8 Why?

11. Example 7: Finding Volumes of Composite Three-Dimensional Figures
Find the volume of the composite figure. Round to the nearest tenth.

12. Example 8
Find the resultant volume when the square prism is removed from the triangular prism.

13. Lesson Quiz: Part I
Find the volume of each figure. Round to the nearest tenth, if necessary.
1. a cube with edge length 22 ft
2. a regular hexagonal prism with edge length 10 ft and height 10 ft
3. a cylinder with diameter 16 in. and height 7 in.
V = 10,648 ft3
V  ft3
V  in3

14. Lesson Quiz: Part II
4. The edge length of the cube is tripled.
Describe the effect on the volume.
5. Given two similar cylinders with V1 = 1000,
r1 =3, and V2 = 8000, find r2
6. Find the volume of the composite
figure. Round to the nearest tenth.
The volume is multiplied by 27.
k = 2, r2 = 6
in3