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

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.

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

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

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

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.

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

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.

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

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

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

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  2598.1 ft3 V  1407.4 in3

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 9160.9 in3