Question: The region bounded by y = r - x, y = 0, and x = 0 is revolved about the y-axis to form a paraboloid.

The region bounded by y = r² - x², y = 0, and x = 0 is revolved about the y-axis to form a paraboloid. A hole, centered along the axis of revolution, is drilled through this solid. The hole has a radius k, 0 < k < r. Find the volume of the resulting ring

(a) By integrating with respect to x

(b) By integrating with
respect to y

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