Volumes

What is the formula for calculating volume of revolution using the disk method?

• V = ∫[a,b] (f(x))^2 dx

• V = π∫[a,b] (f(x))^3 dx

• V = π∫[a,b] (f(x))^2 dy

• V = π∫[a,b] (f(x))^2 dx

When using the washer method, what shapes are the cross-sections perpendicular to the axis of revolution?

• squares

• rectangles

• circles

• triangles

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Calculate the volume of revolution generated by rotating the region bounded by y = x^2, x = 0, and y = 1 about the x-axis using the disk method.

• π/3

• 3π/7

• π/5

• 2π/5

In the disk method, what is the variable of integration typically used for cylindrical shells?

• diameter

• radius

• height

• volume

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Explain the difference between the disk method and the washer method in terms of the shapes being integrated.

• The disk method uses spheres for integration, while the washer method uses cylinders.

• The disk method uses disks for integration, while the washer method uses washers (rings).

• The disk method uses squares for integration, while the washer method uses rectangles.

• The disk method uses triangles for integration, while the washer method uses circles.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Calculate the volume of revolution generated by rotating the region bounded by y = x^2, x = 0, and y = 1 about the x-axis using the washer method.

• pi/5

• 3pi/5

• 4pi/5

• 2pi/5

What is the general formula for calculating volume of revolution using the washer method?

• V = π∫[a,b] (R + r)dx

• V = π∫[a,b] (R^2 + r^2)dx

• V = π∫[a,b] (R - r)dx

• V = π∫[a,b] (R^2 - r^2)dx

When using the disk method, what is the shape of the cross-sections perpendicular to the axis of revolution?

• circle

• ellipse

• triangle

• square

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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

• The volume of revolution is 10π/3 cubic units

• The volume of revolution generated by rotating the region bounded by y = 2x, y = 0, and x = 2 about the y-axis is 8π/3 cubic units.

• The volume of revolution is 6π/3 cubic units

• The volume of revolution is 4π/3 cubic units

Explain the concept of slicing in the context of calculating volume of revolution.

• Slicing only considers the outer surface of the solid, ignoring the inner layers

• Slicing is a method used to break down a solid into infinitesimally thin slices perpendicular to the axis of revolution, allowing for the calculation of volume by summing the volumes of these slices.

• Slicing is a method used to calculate area instead of volume

• Slicing involves rotating the solid around an axis without breaking it down into slices