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 6 Contents Example 1Lateral Area of a Cone Example 2Surface Area of a Cone
Example 6-1a ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of inches. Find the lateral area of the sugar cone. Explore We are given the altitude and the diameter of the base. We need to find the slant height of the cone.
Example 6-1b PlanThe radius of the base, height, and slant height form a right triangle. Use the Pythagorean Theorem to solve for the slant height. Then use the formula for the lateral area of a right circular cone.
Example 6-1c Simplify. Pythagorean Theorem Take the square root of each side. Next, use the formula for the lateral area of a right circular cone. Lateral area of a cone Use a calculator. SolveWrite an equation and solve for.
Example 6-1d ExamineUse estimation to check the reasonableness of this result. The lateral area is approximately Compared to the estimate, the answer is reasonable. Answer: The lateral area is approximately 31.8 square inches.
Example 6-1e A hat for a child’s birthday party has a conical shape with an altitude of 9 inches and a diameter of 5 inches. Find the lateral area of the birthday hat. Answer: 73.4 in 2
Example 6-2a Find the surface area of the cone. Round to the nearest tenth. Surface area of a cone Use a calculator. Answer: The surface area is approximately 20.2 square centimeters.
Example 6-2b Find the surface area of the cone. Round to the nearest tenth. Answer: about 63.6 cm 2