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Lesson 7.4 Surface Area and Volume of Cylinders

Lesson 7.4 Surface Area and Volume of Cylinders. Emma Miller , Emi Oka , Kim Jin, Samuel Koval , Samantha Wolfe, and Zoe Bara. Warm up. Name three cylinders that you see on an everyday experience. How do you define a cylinder in your own words?. Definition of a cylinder.

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Lesson 7.4 Surface Area and Volume of Cylinders

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  1. Lesson 7.4 Surface Area and Volume of Cylinders Emma Miller, Emi Oka, Kim Jin,Samuel Koval, Samantha Wolfe, and Zoe Bara

  2. Warm up • Name three cylinders that you see on an everyday experience. • How do you define a cylinder in your own words?

  3. Definition of a cylinder A cylinder is defined as: A solid that consists of a circular region and its translated image on a parallel plane, with a lateral surface connecting the circular regions.

  4. Bases Bases of cylinders are defined as: The faces formed by the circular region and its translated image.

  5. Altitude An altitude of a cylinder is defined as: A segment that has endpoints in the planes containing the bases and is perpendicular to both planes.

  6. Height The height of a cylinder is defined as: The length of an altitude.

  7. Axis The axis of a cylinder is defined as: The segment joining the centers of the two bases.

  8. Right Cylinder A Right Cylinder is defined as: A cylinder in which the axis of the cylinder is perpendicular to the bases.

  9. Oblique Cylinder An Oblique Cylinder is defined as: A cylinder in which the axis of the cylinder is not perpendicular to the bases.

  10. Net of a Cylinder

  11. 7.4.1 Surface Area of a Right Cylinder The surface area, S, of a right cylinder with lateral area L, base area B, radius r, and height h is:

  12. Example 1 Find the Surface Area using the formula: S=L+2B Lateral Area=6 Base Area=8

  13. Answer and Work 6+(2×8)=96

  14. 7.4.2 Volume of a Cylinder The volume, V, of a cylinder with radius r, height h, and base area B is:

  15. Example 2 Find the volume for a cylinder with the following dimensions, using the formula: Bh=V Base area= 40 Height=5

  16. Answer and Work 40×5=200

  17. Activity! Use the following measurements to find the surface area and volume of paper towel rolls. Base Area1.57 inches Height: 5 inches Lateral Area15.71 inches Radius: .5 inches

  18. How did you get your answer? • Diameter=9 • Height=1.5

  19. Answer and Work Surface area: 15.71+(2×1.57)=18.85 Volume: Bh=V 1.57×5=7.85

  20. Cake Demonstration Use the measurements of the cakeandcalculate the surface area and volume. Radius: 4.5 inches Height: 4 inches Base Area 63.61 Lateral Area113.09

  21. Answer and Work

  22. Correct Answer and Work Surface Area:113.09+(2×63.61)=240.31 Volume: 63.61×4=254.44

  23. Homework Pages 456-457 #14-28 EVEN

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