Area and Volumes AP Calculus

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

• 8π/3
• 32π/5
• 108π/5
• 16π/3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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

• 8π
• 6π
• 2π
• 0

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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

• 5.4
• 30.6
• 96.133
• 108.332

• A
• B
• C
• D

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

• Bounds: [0, 2]; π ∫(4x⁴ - 8)dx
• Bounds: [0, 2]; π ∫((11 - 2x²)² - 9)dx
• Bounds: [-2, 2]; π ∫((11 - 2x²)² - 9)dx
• Bounds: [-2, 2]; π ∫(4x⁴ - 8)dx

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

• 11π/3
• 4π/13
• 3π/7
• 2π/5

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of the solid generated by rotating the region enclosed by y = sin(x) and the x-axis, 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

What is the volume of the solid formed in the second quadrant bounded by the curves         y = 9 – x², the x-axis and the y-axis when it is rotated about the line x = 1?

• 153π/2
• 81π/2
• 648π/5
• 45π/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?

• 72π/5
• 27π/2
• 27π/20
• 9π/10

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Set up but do not solve an integral that will find the volume of the solid described.

• A

• B

• C

• D

• E

Tags

CCSS.7.G.B.6