Rotational Solids and Their Volumes

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 y-axis?

• π²
• 2π²
• 4π²
• 4

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If the region enclosed by the y-axis, y = 2 and the curve y = √x is revolved about the y-axis, what is the volume of the solid generated?

• 32π/5
• 16π/3
• 16π/5
• 8π/3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If the region enclosed by y = 1/x, y = 0 between x = 1 and x = 5 is revolved about the x-axis, what is the volume of the solid generated?

• 4π/5
• 2π/5
• 3π/5
• πln(5)

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Find the volume of when region bounded by   y = 4/x, x = 4 and y = 2 is revolved about the y-axis.

• 8π
• 16π
• 16π/3
• 24π

Find the volume of when the region bounded by y = x³, x = 4 and the x-axis is revolved about the y-axis.

• 2048π/5
• 3072π/5
• 1024π/5
• 64π

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 = 0, x = 3 and y = 5x² is revolved about the y-axis, what is the volume of the solid generated?

• 405π/2
• 405π/4
• 90π
• 810π

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