Volume of Revolution using the Washer Method

This video tutorial explains how to determine the volume of a solid of revolution using the washer method. The example involves rotating a region bounded by specific curves about a line parallel to the x-axis. The tutorial covers graphing the region, determining the outer and inner radii, setting up the integral, and evaluating it to find the volume. The final result is presented both as an exact value and a decimal approximation.

What is the primary method used in this tutorial to find the volume of a solid of revolution?

• Shell Method

• Disk Method

• Cavalieri's Principle

• Washer Method

Which axis is the region rotated about in this example?

• x = 2

• y = 0

• y = 3

• x = 0

What is the equation of the curve that forms the boundary of the region?

• y = 12x^2

• y = 6x^2

• y = 9x^2

• y = 3x^2

How is the outer radius determined in this problem?

• It varies with x

• By subtracting the function value from 3

• It is a constant value of 3

• By adding the function value to 3

What is the expression for the inner radius in this example?

• 12x^2 + 3

• 3 + 12x^2

• 3 - 12x^2

• 12x^2 - 3

What are the limits of integration for the volume integral?

• 0 to 1

• 0 to 2

• 0 to 12

• 0 to 3

What is the integrand in the volume integral?

• (3 - 12x^2)^2 - 3^2

• 3^2 - (3 - 12x^2)^2

• (3 - 12x^2)^2 + 3^2

• 3^2 + (3 - 12x^2)^2

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

• 32π/5

• 20π/5

• 8π/5

• 16π/5

What is the decimal approximation of the volume?

• 20.1062

• 25.1062

• 15.1062

• 30.1062

What is the unit of the calculated volume?

• Square units

• No units

• Cubic units

• Linear units