1. 7.4: SURFACE AREA AND VOLUME OF CYLINDERS Expectation: G1.8.1: Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres. 2/22/20167.4: Surface Area and Volume of Cylinders

2. A regular hexagonal pyramid has base perimeter of 72 inches and slant height of 14 inches. Determine the exact volume of the pyramid.

4. What will we learn today? 2/22/20167.4: Surface Area and Volume of Cylinders

5. Cylinder Defn: A cylinder is the union of a circular region, its translated image in space and all points in between. 2/22/20167.4: Surface Area and Volume of Cylinders

6. Anatomy of a Cylinder 2/22/20167.4: Surface Area and Volume of Cylinders _________

7. Anatomy of a Cylinder 2/22/20167.4: Surface Area and Volume of Cylinders Lateral surface

8. Anatomy of a Cylinder 2/22/20167.4: Surface Area and Volume of Cylinders _________ The height of a cylinder is the length of one of its altitudes.

9. Anatomy of a Cylinder 2/22/20167.4: Surface Area and Volume of Cylinders The ______of a cylinder is the segment with its endpoints at the centers of the bases.

10. Right Cylinders A cylinder is right if its axis is ______________ to its bases. 2/22/20167.4: Surface Area and Volume of Cylinders

11. Oblique Cylinders A cylinder is oblique if its axis is oblique to its ______. 2/22/20167.4: Surface Area and Volume of Cylinders

12. Lateral and Surface Areas of a Right Cylinder a. Sketch a net for a right cylinder with radius r and height h. b. What is the lateral area of the cylinder? c. What is the surface area of the cylinder? 2/22/20167.4: Surface Area and Volume of Cylinders

13. Lateral and Surface Areas of a Right Cylinder Let L be the lateral area and S be the surface area of a right cylinder with radius r and height h. Then L = _______ and S = ______________ 2/22/20167.4: Surface Area and Volume of Cylinders

14. Volume of a Cylinder Let V be the volume of a cylinder with radius r and height h. Then V=_________. 2/22/20167.4: Surface Area and Volume of Cylinders

15. A cylindrical water tank has a diameter of 30 feet and a height of 100 feet. If 1 cubic foot of water is 7.48 gallons, how many gallons of water will the tank hold? 2/22/20167.4: Surface Area and Volume of Cylinders

16. An oblique cylinder has a height of 10 inches and its base has radius of 5 inches. A Right cylinder has radius of 5 inches and its height is 10 inches. A right rectangular prism has a base with dimensions 5 inches by 5π inches and a height of 10 inches. Compare the volumes of the three figures and give a justification. 2/22/20167.4: Surface Area and Volume of Cylinders

17. The volume of a right cylinder is 125π cubic cm. If the height of the cylinder is 5 cm, what is the surface area of the right cylinder? 2/22/20167.4: Surface Area and Volume of Cylinders

18. What is the volume of a cylinder with a height of 16 and a base area of 25π? A. 5π B. 25π C. 50π D. 200π E. 400π 2/22/20167.5: Surface Area and Volume of Cones

19. Assignment pages 456-458, # 13-29(odd), 30-32 (all), 35-38 2/22/20167.4: Surface Area and Volume of Cylinders