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S OLIDS OF R EVOLUTION 4-G. Disk method Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate.

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Presentation on theme: "S OLIDS OF R EVOLUTION 4-G. Disk method Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate."— Presentation transcript:

1 S OLIDS OF R EVOLUTION 4-G

2 Disk method

3 Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate in terms of x Revolve about a vertical axis Slice perpendicular to axis – slices horizontal Integrate in terms of y

4 Washer Method

5 Volume of Washer: Horizontal axis of revolution Slice with rectangle perpendicular to axis Integrate in terms of x Vertical axis of revolution Slice with rectangles perpendicular to axis Integrate in terms of y Find Volume – Washer Method

6 1) Find the volume of the solid is bounded by the curve y = x and the x-axis between x = 0 and x = 1 rotated about the x-axis

7 2)Find the volume of the solid when the region bounded by is revolved about the x-axis

8 3) Find the volume of the solid generated when the region bounded by is revolved about the x-axis

9 4) Find the volume of the solid generated when the region bounded by is revolved about the line y = 4

10 5) Set up the integrals for finding the volume of the solid formed by revolving the region formed by a) About the x-axisb) about y = -1

11 6) Find the volume of the solid generated when the region bounded by is revolved about the line y = 3

12 7) Find the volume of the solid generated when the region bounded by is revolved about the y-axis

13 H OME W ORK Finding Volumes of solids using washers and disks worksheet

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