Cross Sections Retake prep video

What is the general formula for finding the volume of a solid using cross-sections perpendicular to the x-axis?

• V = ∫[a,b] A(y) dy

• V = ∫[a,b] A(x) dx

• V = ∫[c,d] A(x) dx

• V = ∫[c,d] A(y) dy

For the solid bounded by y = sqrt(x), x = 4, and the x-axis, with square cross-sections perpendicular to the x-axis, what is the side length 's' of a square cross-section?

• s = x

• s = x^2

• s = sqrt(x)

• s = 4

What is the volume of the solid bounded by y = sqrt(x), x = 4, and the x-axis, using square cross-sections perpendicular to the x-axis?

• 4

• 8

• 16

• 32

For the solid bounded by the x-axis, y-axis, and the line y = 4 - x/2, with semicircular cross-sections perpendicular to the x-axis, what represents the diameter 's' of a semicircle cross-section?

• s = x

• s = 4 - x/2

• s = 8

• s = 4

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What is the area of a semicircular cross-section with diameter 's'?

• A = pi * s^2

• A = 1/2 * pi * s^2

• A = 1/4 * pi * s^2

• A = 1/8 * pi * s^2

What is the area function A(x) for the semicircular cross-sections, given that the diameter 's' is equal to y, and y = 4 - x/2?

• A(x) = 1/8 * pi * (4 - 1/2 x)^2

• A(x) = 1/8 * pi * (4 - x)^2

• A(x) = 1/2 * pi * (4 - 1/2 x)^2

• A(x) = 1/4 * pi * (4 - x/2)^2

When expanding the term (4 - 1/2 x)^2, what is the resulting polynomial?

• 1/4 x^2 - 2x + 16

• 1/4 x^2 - 4x + 16

• 1/2 x^2 - 4x + 16

• 1/4 x^2 - 8x + 16

What is the final volume of the solid bounded by the x-axis, y-axis, and the line y = 4 - x/2, using semicircular cross-sections perpendicular to the x-axis?

• 8pi/3

• 16pi/3

• 32pi/3

• 64pi/3