Solids of Revolution Geometry

Graph the region bounded by y=5/(1+x), y=2 and the x-axis. Select the best method to use when rotating about the y-axis.

• Disk Method

• Washer Method

• Shell Method

Graph the region bounded by y=5/(1+x), y=2 and the x-axis. Select the best method to use when rotating about the line y = 6.

• Disk Method

• Washer Method

• Shell Method

Graph the region bounded by y=5/(1+x), y=2 and the x-axis. Select the best method to use when rotating about the line x = -2

• Disk Method

• Washer Method

• Shell Method

Graph the region bounded by by y=2x²- x³ and y=0. Select the best method to use when rotating about the line x = -2

• Disk Method

• Washer Method

• Shell Method

Find the volume of the solid obtained by rotating about the y-axis bounded by y=2x²- x³ and y=0.

• 8/5 or 1.6

• 8/5 pi or 5.027

• 16/5 pi or 10.053

• 18/5 pi or 11.310

Use the shell method to find the volume of the solid obtained by rotating the region bounded by y=x³, y=8, and x=0 about the x-axis. Sketch the region on scratch paper.

• 344.677

• 54.857

• 172.339

• 75.398

Use the shell method to find the volume of the solid obtained by rotating the region bounded by y=(x-1)^1/2, y=0, and x=5 about y=3. Sketch the region on scratch paper.

• 6pi

• 8pi

• 12pi

• 24pi

Use the shell method to find the volume of the solid obtained by rotating the region bounded by y=3+2x-x² and x+y=3 about the y-axis. Sketch the region on scratch paper.

• 344.677

• 54.857

• 172.339

• 75.398

Find the volume of the solid obtained by rotating about the y-axis bounded by y=3x-x^2 and y=0.

• 87.965

• 84.823

• 42.412

• 56.549

Find the volume of the solid obtained by rotating about the line x=1 bounded by y=1-x^2 and the x-axis.

• 3pi

• 8pi/3

• 7pi/3

• 2pi