Volume The Disk Method Section 6 2 AP

Volume: The Disk Method Section 6. 2 AP Calc

Disk Method Horizontal axis of revolution: Vertical axis of revolution:

1 Find the volume of the solid formed by rotating the region bounded by and the x-axis about the x-axis.

2 Find the volume of the solid formed by rotating the region bounded by x=0, x=4, and the x-axis about the x-axis.

3 Find the volume of the solid formed by rotating the region bounded by y=0, y=4, and the y-axis about the y-axis.

4 Find the volume of the solid formed by rotating the region bounded by and the line y=3 about the line y=3.

5 Find the volume of the solid formed by rotating the region bounded by y=2, x=4, and x=25 about the line y=2.

Washer Method

6 Find the volume of the solid formed by rotating the region bounded by y=x 2 and y=x 3 about the x-axis.

7 Find the volume of the solid formed by rotating the region bounded by y=x 2 and y=x 3 about the y-axis.

8 Find the volume of the solid formed by rotating the region bounded by y=4 -x 2 and y=3 about the line y=6.

9 Given the region bounded by y=x 2, the xaxis and x=2, find the volume of the region rotated about A) the x-axis B) the y-axis C) the line x=4

The region bounded by y=x 2, the x-axis, and x=2 is the base of a solid. Find the value of this solid if it has A) square cross sections perpendicular to the x-axis B) equilateral triangle cross sections perpendicular to the x-axis