1. 3/17/20167.5: Surface Area and Volume of Cones Expectation: G1.8.1: Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres. G2.1.3: Know and use the relationship between the volumes of pyramids and prisms (of equal base and height) and cones and cylinders (of equal base and height).

2. 3/17/20167.5: Surface Area and Volume of Cones Cone Defn: A cone is a 3 dimensional figure that is the union of a circular region (base) and a curved lateral surface that connects the base to a single point (vertex) not in the plane of the base.

3. 3/17/20167.5: Surface Area and Volume of Cones Altitude of a Cone The altitude of a cone is the segment with one endpoint at the vertex and the other endpoint in the plane of the base such that it is perpendicular to the base.

4. 3/17/20167.5: Surface Area and Volume of Cones Height of a Cone The height of a cone is the length of its altitude.

5. 3/17/20167.5: Surface Area and Volume of Cones Axis of a Cone The axis of a cone is a segment whose endpoints are the center of the base and the vertex of the cone

6. 3/17/20167.5: Surface Area and Volume of Cones Right Cone A cone is a ______ cone if its axis is also the altitude.

7. 3/17/20167.5: Surface Area and Volume of Cones Oblique Cone A cone is oblique if its axis is _____ its altitude.

8. 3/17/20167.5: Surface Area and Volume of Cones Slant Height of a Cone A slant height is a segment whose endpoints are the vertex and a point on the circle of the base, such that the segment is ________________ to the base edge.

9. 3/17/20167.5: Surface Area and Volume of Cones Slant Height The length of a slant height is denoted l. l

10. 3/17/20167.5: Surface Area and Volume of Cones Surface area of a Right Cone Let L be the lateral area and S be the surface area of a right cone with radius r and slant height. Let L be the lateral area and S be the surface area of a right cone with radius r and slant height l. Then L = __________ and S = _________________.

11. 3/17/20167.5: Surface Area and Volume of Cones A right cone has lateral area of 84π. If the slant height is 12 cm, what is the exact surface area of the cone?

12. 3/17/20167.5: Surface Area and Volume of Cones Volume of a Cone Let V be the volume of a cone with radius r and height h. Then V =___________.

13. 3/17/20167.5: Surface Area and Volume of Cones A paper cup is in the shape of a cone. If the diameter of the cone is 7cm and the height is 10cm, what is the capacity (in mL) of the cup?

14. A right rectangular prism is 4 inches long, 2 inches wide and 2.5 inches high. A right cone is 3 inches tall and its base has a radius of 2.5 inches. If the prisms was made of ice and it melted, would the cone be able to contain all of the water from the prism? 3/17/20167.5: Surface Area and Volume of Cones

15. What is the volume of a cylinder with a height of 16 and a base area of 25 π? A. 5π B. 25π C. 50π D. 200π E. 400π 3/17/20167.5: Surface Area and Volume of Cones

16. 3/17/20167.5: Surface Area and Volume of Cones Assignment pages 465-467, #11-35 (odds), 32