Question: Let R be the region in the first quadrant bounded by the circle x 2 + y 2 = r 2 and the coordinate axes.

Let R be the region in the first quadrant bounded by the circle x² + y² = r² and the coordinate axes. Find the volume of a hemisphere of radius r in the following ways.

a. Revolve R about the x-axis and use the disk method.

b. Revolve R about the x-axis and use the shell method.

c. Assume the base of the hemisphere is in the xy-plane and use the general slicing method with slices perpendicular to the xy-plane and parallel to the x-axis.

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