Volumes of Revolution

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by f(x) = x² from [0, 2] around the x-axis. 

• 8π/3
• 32π/5
• 108π/5
• 16π/3

NO CALCULATOR: Find the volume of the solid generated by revolving the area bounded by y = x² from [0, 2] around the y-axis. 

• 8π
• 6π
• 2π
• 0

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

• A
• B
• C
• D

What is the volume of the solid generated by rotating the region enclosed by y = sin(x), from x = 0 to x = π about the x-axis?

• π²

• π²/2

• 4π²

• π/2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If the region enclosed by y = 3x², y = 3 is revolved about the x-axis, what is the volume of the solid generated from -1 to 1?

• 72π/5
• 27π/2
• 27π/20
• 9π/10