1. Miss Battaglia AP Calculus

2. Rotate around the x-axis and find the volume of y= 1 / 2 x from 0 to 4.

3. If a region in the plane is revolved about a line, the resulting solid is a solid of revolution, and the line is called the axis of revolution. The simplest such solid is a right circular cylinder or disk (formed by revolving a rectangle about an axis adjacent to one side of the rectangle. Volume of disk = (area of disk)(width of disk) = πR 2 Δx ΔV = πR 2 Δx

5. The approximation of the volume of a solid becomes better as ||Δ||  0 (n  ∞). Volume of a solid = Volume of a Solid Representative Element Solid of revolution

6. To find the volume of a solid of revolution with the disk method, use one of the following: Horizontal Axis of Revolution Vertical Axis of Revolution

7. Find the volume of a solid formed by revolving the region bounded by the graph of and the x-axis (0 < x < π) about the x-axis.

8. Find the volume of a solid formed by revolving the region bounded by and g(x)=1 about the line y=1.

9. 1. y = - x + 1 revolved about the x-axis from 0 to 1 2. y = 4 – x 2 revolved about the x-axis from 0 to 2 3. revolved about the x-axis from 1 to 4 4. revolved about the x-axis from 0 to 3 5. y = 2 and from -3 to 3 6. revolved about the x-axis from 0 to 4 7., y = 0 from 0 to 3 8. y = 2x 2, y=0, from 0 to 2

10. The disk method can be extended to cover solids of revolution with holes by replacing the representative disk with a washer.

11. Find the volume of the solid formed by revolving the region bounded by the graph of and about the x-axis.

12. Find the volume of a solid formed by revolving the region bounded by the graph of y=x 2 +1, y=0, x=0, and x=1 about the y-axis.

13. A manufacturer drills a hole in the middle of a metal sphere of radius 5 in. The hole has a radius of 3 in. What is the volume of the resulting metal ring?

14.  Read 7.2 Page 465 #1-9 odd, 11, 13