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Contents Lesson 12-1Three-Dimensional Figures Lesson 12-2Nets and Surface Area Lesson 12-3Surface Areas of Prisms Lesson 12-4Surface Areas of Cylinders Lesson 12-5Surface Areas of Pyramids Lesson 12-6Surface Areas of Cones Lesson 12-7Surface Area of Spheres

Lesson 4 Contents Example 1Lateral Area of a Cylinder Example 2Surface Area of a Cylinder Example 3Find Missing Dimensions

Example 4-1a A fruit juice can is cylindrical with aluminum sides and bases. The can is 12 centimeters tall, and the diameter of the can is 6.3 centimeters. How many square centimeters of aluminum are used to make the sides of the can? The aluminum sides of the can represent the lateral area of the cylinder. If the diameter of the can is 6.3 centimeters, then the radius is 3.15 centimeters. The height is 12 centimeters. Use the formula to find the lateral area.

Example 4-1b Lateral area of a cylinder Use a calculator. Answer: About square centimeters of aluminum are used to make the sides of the can.

Example 4-1c A set of toy blocks are sold in a cylindrical shape container. A product label wraps around all sides of the container without any overlaps or gaps. How much paper is used to make the label the appropriate size if the diameter of the container is 12 inches and the height is 18 inches? Answer: about in 2

Example 4-2a Find the surface area of the cylinder. The radius of the base and the height of the cylinder are given. Substitute these values in the formula to find the surface area.

Example 4-2b Surface area of a cylinder Use a calculator. Answer: The surface area is approximately square feet.

Example 4-2c Find the surface area of the cylinder. Answer: about ft 2

Example 4-3a Use the formula for surface area to write and solve an equation for the radius. Surface area of a cylinder Substitution Simplify. Find the radius of the base of a right cylinder if the surface area is square feet and the height is 10 feet. Divide each side by

Example 4-3b Subtract 264 from each side. Factor. Solve. Since a radius of a circle cannot have a negative value, –22 is eliminated. Answer: The radius of the base is 12 feet.

Example 4-3b Answer: 14 in. Find the radius of the base of a right cylinder if the surface area is square inches and the height is 22 inches.

End of Lesson 4

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