Solids of Revolution Geometry

The base of a solid is bounded by the lines y = x/2 - 3 and y = -x/2 + 3 and the y-axis. Cross sections perpendicular to the x-axis are semicircles. Find the volume of this solid.

• 9π

• 18π

• 36π

• 12π

Determine the volume of the region bounded by y = x² - 2x and y = x that is rotated about y = 4.

• 130.062

• 30.6

• 96.133

• 108.332

What integral (Disk/Washer) would allow you to find the volume of the region bounded by y = 2x² and y = 8 around the line y = 11.

• Limits: [0, 2]; π ∫(4x⁴ - 8)dx

• Limits: [0, 2]; π ∫((11 - 2x²)² - 9)dx

• Limits: [-2, 2]; π ∫((11 - 2x²)² - 9)dx

• Limits: [-2, 2]; π ∫(4x⁴ - 8)dx

The base of a solid is an ellipse with equation 9x² + y² = 9. Parallel cross sections perpendicular to the x-axis are squares. Find the volume of this solid.

• 96

• 48

• 24

• 12

• none of these

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.

• 
• 
• 
• 

• 71π/5

• 224π/15

• 15π

• 211π/15

Find the volume of the solid generated by rotating the region bounded by the graphs of y = 1/x, y = 0, x = 2, and x = 6 around the line x = -1.

• 2π(4+ln 6)

• 2π(4 - ln 3)

• 2π(4 + ln 3)

• π(8 + ln 6)

Find the volume of the solid using the Shell Method generated by revolving the region bounded by the graphs of y=cos(x/2), x = 0, and y = 0 in the first quadrant about the line x = π. (SET UP ONLY)

• 
• 
• 
•