Volume Calculation Using the Washer Method

The video tutorial explains how to use the washer method to calculate the volume of a solid formed by rotating a region bounded by two functions around the y-axis. It covers setting up the problem, determining the outer and inner radii, solving the integral, and calculating the final volume, providing both exact and approximate results.

What method is used to find the volume of the solid formed by rotating the region bounded by the given curves?

• Cavalieri's Principle

• Washer Method

• Shell Method

• Disk Method

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Which two functions define the region that is rotated about the y-axis?

• y = sqrt(x) and y = x^4

• y = x^2 and y = x^3

• y = x and y = x^2

• y = x^3 and y = x^4

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

What is the significance of the representative rectangle in the washer method?

• It helps in visualizing the axis of rotation.

• It represents the height of the solid.

• It is used to calculate the surface area.

• It helps in setting up the integral for volume.

How is the outer radius, R(y), determined in this problem?

• By finding the distance from the x-axis to the curve y = sqrt(x)

• By finding the distance from the y-axis to the curve y = x^4

• By finding the distance from the x-axis to the curve y = x^4

• By finding the distance from the y-axis to the curve y = sqrt(x)

What is the expression for the inner radius, r(y), in terms of y?

• r(y) = y^(1/2)

• r(y) = y^3

• r(y) = y^(1/4)

• r(y) = y^2

What is the integral setup for finding the volume of the solid?

• Integral from 0 to 1 of (R(y)^2 + r(y)^2) dy

• Integral from 0 to 1 of (R(y)^2 - r(y)^2) dy

• Integral from 0 to 1 of (R(y) - r(y)) dy

• Integral from 0 to 1 of (R(y) + r(y)) dy

What is the antiderivative of y^(1/2) with respect to y?

• y^(3/2) / (3/2)

• y^(1/2) / (3/2)

• y^(3/2) / (2/3)

• y^(1/2) / (1/2)

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

What is the exact volume of the solid in cubic units?

• 7π/15

• 2π/9

• 5π/12

• 3π/10

Tags

CCSS.6.G.A.2

CCSS.5.MD.C.5B

What is the approximate volume of the solid in cubic units?

• 1.8901

• 1.2345

• 1.6789

• 1.4661

What is the common denominator used to combine the fractions 2/3 and 1/5?

• 15

• 10

• 25

• 20