Volume of Solids of Revolution

Find the volume of the solid generated by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis using the disk method.

• (32/5)π

• 4π

• 8π

• 16π

Tags

CCSS.HSG.GMD.A.3

Calculate the volume of the solid formed by rotating the area enclosed by y = 4 - x^2, y = 0, and x = 1 about the y-axis using the washer method.

• The volume of the solid is (8/15) * pi units^3

• The volume of the solid is (64/15) * pi units^3

• The volume of the solid is (32/15) * pi units^3

• The volume of the solid is (16/15) * pi units^3

Tags

CCSS.HSG.GMD.A.3

Determine the volume of the solid obtained by rotating the region bounded by y = x^3, y = 0, and x = 1 about the y-axis using the disk method.

• π/4

• 3π/5

• π/5

• 2π/5

Tags

CCSS.HSG.GMD.A.3

Compute the volume of the solid created by revolving the area between y = 2x, y = 0, and x = 2 about the x-axis using the washer method.

• 32π/3

• 24π/3

• 16π/3

• 40π/3

Tags

CCSS.HSG.GMD.A.3

Find the volume of the solid generated by rotating the region enclosed by y = 3x^2, y = 0, and x = 1 about the y-axis using the disk method.

• The volume of the solid generated is 9π/5 cubic units.

• The volume of the solid generated is 12π/5 cubic units.

• The volume of the solid generated is 5π/3 cubic units.

• The volume of the solid generated is 7π/5 cubic units.

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Calculate the volume of the solid formed by rotating the area bounded by y = 1 - x^2, y = 0, and x = 1 about the x-axis using the washer method.

• 6/15π

• 4/15π

• 8/15π

• 2/15π

Tags

CCSS.HSG.GMD.A.3

Determine the volume of the solid obtained by rotating the region between y = x^2, y = 0, and x = 2 about the y-axis using the disk method.

• 6.4 * pi

• 3.6 * pi

• 4.2 * pi

• 12.8 * pi

Tags

CCSS.HSG.GMD.A.3

Compute the volume of the solid created by revolving the area enclosed by y = 2 - x^3, y = 0, and x = 1 about the y-axis using the washer method.

• The volume of the solid is approximately 5.123

• The volume of the solid is infinite

• The volume of the solid is exactly 2.5

• The volume of the solid is approximately 3.490

Tags

CCSS.HSG.GMD.A.3

Find the volume of the solid generated by rotating the region bounded by y = 4x, y = 0, and x = 2 about the x-axis using the disk method.

• The volume of the solid generated is 16pi cubic units.

• The volume of the solid generated is 128pi cubic units.

• The volume of the solid generated is 32pi cubic units.

• The volume of the solid generated is 64pi cubic units.

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Calculate the volume of the solid formed by rotating the area between y = 2x^2, y = 0, and x = 1 about the y-axis using the washer method.

• 2.094 cubic units

• 3.142 cubic units

• 4.712 cubic units

• 1.047 cubic units

Tags

CCSS.HSG.GMD.A.3