Learn and apply the formula for the surface area and volume of a prism. Learn and apply the formula for the surface area and volume of a cylinder. Objectives (see page 680 and page 697) Unit 10 Prisms and Cylinders (4/11/12)

lateral face lateral edge right prism oblique prism altitude surface area volume lateral surface axis of a cylinder right cylinder oblique cylinder Vocabulary (see page 680 and page 697) Unit 10 Prisms and Cylinders (4/11/12)

Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face. (see page 680)

An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude. Surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. (see page 680)

The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. 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. A right prism and an oblique prism with the same base and height have the same volume. (see page 697 and page 699) Cavalieri ’ s principle also relates to cylinders. The two stacks have the same number of CDs, so they have the same volume.

The lateral surface of a cylinder is the curved surface that connects the two bases. The axis of a cylinder is the segment with endpoints at the centers of the bases. The axis of a right cylinder is perpendicular to its bases. The axis of an oblique cylinder is not perpendicular to its bases. The altitude of a right cylinder is the same length as the axis. (see page 681)

** The surface area of a right rectangular prism with length ℓ, width w, and height h can be written as S = 2ℓw + 2wh + 2ℓh. (see page 680 and page 697) Unit 10 Prisms and Cylinders (4/11/12)

(see page 681 and page 699)

Example 1A: Finding Lateral Areas and Surface Areas of Prisms Find the lateral area, surface area, and volume of the right rectangular prism. Round to the nearest tenth, if necessary. (see page 681)

Check It Out! Example 1 (see page 681) Find the lateral area, surface area, and volume of a cube with edge length 8 cm.

Example 1C: Finding Volumes of Prisms (see pages ) Find the lateral area, surface area, and volume of the right regular hexagonal prism. Round to the nearest tenth, if necessary.

Check It Out! Example 1 (see page 698) Find the lateral area, surface area, and volume of a triangular prism with a height of 9 yd whose base is a right triangle with legs 7 yd and 5 yd long.

Example 2A: Finding Lateral Areas and Surface Areas of Right Cylinders (see page 682) Find the lateral area, surface area, and volume of the right cylinder. Give your answers in terms of .

Check It Out! Example 2 (see page 682) Find the lateral area, surface area, and volume of a cylinder with a base area of 49  and a height that is 2 times the radius.

Example 3A: Finding Volumes of Cylinders (see page 699) Find the lateral area, surface area, and volume of the cylinder. Give your answers in terms of  and rounded to the nearest tenth.

Example 4: Exploring Effects of Changing Dimensions (see page 683) The edge length of the cube is tripled. Describe the effect on the surface area.

Check It Out! Example 4 (see page 700) The length, width, and height of the prism are doubled. Describe the effect on the volume.

Check It Out! Example 4 (see page 683) The height and diameter of the cylinder are multiplied by. Describe the effect on the surface area.

Example 4: Exploring Effects of Changing Dimensions (see page 700) The radius and height of the cylinder are multiplied by. Describe the effect on the volume.