10 4 Surface Area of Prisms and Cylinders

10. 4 Surface Area of Prisms and Cylinders Geometry

Definitions: n n Lateral face: not the base Lateral edge: not an edge of the base Right prism: All lateral faces are rectangles Oblique prism: has at least one nonrectangular lateral face

Diagram:

Definitions n Altitude: the perpendicular segment joining the planes of the bases (the height of the prism)

Definition n Surface Area: the total area of all faces and curved surfaces of a threedimensional figure.

Formulas n n Lateral Area of Right Prisms L=Ph Surface Area of Right Prisms S=L+2 B or S=Ph+2 B

Examples: n Find the lateral area and surface area of the right prism.

Example: n Find the lateral area and surface area of a right regular triangular prism with height 20 cm and base edges 10 cm.

Example: n Find the lateral and surface area of a cube with edge length 8 cm.

Definitions: n n Lateral surface: cylinder is the curved surface that connects the two bases. Axis of a cylinder: the segment with endpoints at the centers of the bases. (also called height) Right Cylinder: the axis is perpendicular to the bases Obliques Cylinder: the axis is not perpendicular to the bases.

Diagram:

Formulas: n

Example: n Find the lateral and surface area for the right cylinder.

Example: n

Example: n

Examples: n Find the surface area of the composite figure.

Example: n Find the surface area of the composite figure.

Example: n The edge length of the cube is tripled. Describe the effect on the surface area.

Example: n The height and the diameter of the cylinder are multiplied by ½. Describe the effect on the surface area.

Example: n A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon. Which tent requires less nylon to manufacture?