1. 12.6 Surface Areas of Cones

2. Objectives  Find lateral areas of cones.  Find surface areas of cones.

3. Cones Circular Cone Circular Cone is a three- dimensional shape with one circular base and a vertex that is not in the same plane as the base.

4. Parts of cones ➔ Characteristics of Cones: The base is a a circle and the vertex is the point V. Axis- segment with endpoints at vertex and the center of the base. Altitude- Segment from vertex and perpendicular to the base.

5. Oblique Cone – a cone whose axis is not perpendicular (or an altitude) to the base.

6.  Right Cone  Right Cone is a cone with an axis that is also an altitude.

7. Lateral Area of a Cone If a right circular cone has a lateral area of a L square units, a slant height of a l units, and the radius of the base is r units, L= πr l

8. Example # 1: LAMPS: Diego has a conical lamp shade with an altitude of 6 inches and a diameter of 12 inches. Find the lateral area of the lampshade. Explore Explore We are given the altitude and the diameter of the base. We need to find the slant height of the cone.

9. Plan Plan The 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 the a right circular cone.

10. Solve Write an equation and solve for l. l² = 6² + 6² Pythagorean Theorem l² = 72 Simplify l = √72 or 6√2 Take the square root of each side.

11. Next, use the formula for the lateral area of a right circular cone. L=  r l Lateral area of a cone ≈  (6) (6 √2)r = 6, l = 6√2 ≈ 159.9 Use a calculator. The lateral area is approximately 159.9 square inches

12. Surface Area of a Cone If a right circular cone has a surface area of T square units, a slant height of l units, and the radius of the base is r units, then T= πr l + πr ²

13. Example 2: Surface Area of a Cone Find the surface area of the cone. T = πr l + πr² = π(4.7)(13.6) + π(4.7)² ≈ 270.2 Surface area of a cone r = 4.7, l = 13.6 Use a calculator. The surface area is approximately 270.2 square centimeters.

14. Assignment: Page 668 – 669 # 7 - 22