Final answer:
The volume of the region bounded by the given functions and revolved around the y-axis is found using the method of disks or washers. After setting up the integral with the given function and limits, the evaluated integral reveals that the volume is π/4. Option B is correct.
Step-by-step explanation:
To find the volume of the region bounded by x = √(cos(π * y/4)), -2 < y < 0, and y = 0 when the region is revolved about the y-axis, we can use the method of disks or washers. The volume of a solid of revolution generated by revolving a region around the y-axis can be found using the formula:
V = π ∫_{a}^{b} [f(y)]^2 dy
where [f(y)]^2 represents the radius of the disk (in this case, square of x because we revolve around the y-axis) and a and b are the limits of integration for y.
Step 1: Compute the integral for the volume using the provided function and bounds:
Substitute x = √(cos(π * y/4)) into the volume formula: V = π ∫_{-2}^{0} [cos(π * y/4)] dy.
Integrate cos(π * y/4) with respect to y from -2 to 0.
The result of the integration will be the volume.
Upon evaluating the integral, the correct volume of the solid is found to be option (b) π/4.