10.2.1 Surface Area of Prisms and Cylinders Key Objectives • Learn and apply the formula for the surface area of a prism. • Learn and apply the formula for the surface area of a cylinder. Key Terms • A lateral face is not a base. • 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.
• An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. • Surface area is the total area of all faces and curved surfaces of a three-dimensional figure. • 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. Formulas • Lateral Area of a Right Prism The lateral area of a right prism with base perimeter P and height h is L = Ph . • Surface Area of a Right Prism The surface area of a right prism with lateral area L and base area B is S = L + 2 B , or S = Ph + 2 B . • Surface Area of a Cube The surface area of a cube with edge length s is S = 6 s 2 . • Lateral Area of a Right Cylinder The lateral area of a right cylinder with radius r and height h is L = 2 πrh . • Surface Area of a Right Cylinder The surface area of a right cylinder with lateral area L and base area B is S = L + 2 B , or S = 2 πrh + 2 πr 2 . Example 1 Finding Lateral Areas and Surface Areas of Prisms The lateral area of a right prism is equal to the
product of the perimeter of the base and the height. The surface area of a right prism is equal to the lateral area plus the area of the two bases. The surface area of a cube is equal to the length of an edge cubed.
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