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 bounded region around a vertical axis. It covers setting up the integral, graphing the region, determining the outer and inner radii, solving the integral, and evaluating the result. The tutorial provides both exact and approximate volume calculations.

What method is used to determine the volume of the solid in this problem?

• Cavalieri's principle

• Washer method

• Shell method

• Disk method

What is the axis of rotation for the region bounded by the given equations?

• y = 0

• x = 0

• x = 5

• x = 4

In the washer method, with respect to which variable is the integration performed?

• Theta

• X

• Y

• Z

What is the outer radius, Big R of Y, expressed as a function of Y?

• 5 + y^2 / 4

• 5 - y^2 / 4

• y^2 / 4

• y / 2

What is the constant value of the inner radius, little r of Y?

• 1

• 5

• 0

• 2

What is the first step in evaluating the integral for the volume?

• Calculating the definite integral

• Finding the anti-derivative

• Squaring the binomial

• Simplifying the terms

What is the result of squaring the binomial (5 - y^2 / 4)?

• 25 - 5y^2 + 1/16y^4

• 25 - 10y^2 + 1/16y^4

• 25 - 5y^2 + 1/4y^4

• 25 - 10y^2 + 1/4y^4

What is the exact volume of the solid formed by rotating the region?

• 832 Pi / 15 cubic units

• 174.5037 cubic units

• 832 Pi cubic units

• 174.5037 Pi cubic units

What is the approximate volume of the solid in decimal form?

• 832 cubic units

• 174.5037 cubic units

• 832 Pi / 15 cubic units

• 174.5037 Pi cubic units

What is the purpose of using the washer method in this problem?

• To find the centroid of the region

• To calculate the perimeter of the region

• To determine the volume of the solid

• To find the surface area of the solid