Quote of the Day: "God is a child; and when he began to play, he cultivated mathematics. It is the most godly of man's games." -- V. Erath Objectives: The student will compute the volume of solids of revolution using the washer method (slicing with a hole in it), the disk method, and the shell method. The student will compute the volume of solids of revolution rotated about a line other than the x- or y-axis. 1. Collect homework. 2. Shell Method Use the Shell Method if (1) you have a function in terms of x and rotation is around the y-axis or (2) you have a function in terms of y and rotation is around the x-axis. Find the volume of one shell and then add them up. To find the volume of a cylindrical shell, take the circumference of the circle, multiply it by the height to get the lateral surface area, then multiply by the thickness. Then create a Riemann sum and take the limit. 3. To help see the shell method – (a) Bring in Russian stacking dolls (Use the lower half of the dolls – they look like shells).
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6. Distribute Quiz on Volumes of Solids of Revolution7. Click here for visualization of Solids 8. Assignment: Finish p. 456 (2, 5, 11, 22, 25, 35, 36) |