Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^5, y=x, y=1y=1, and the y-axis and whose cross-sections perpendicular to the x axis are squares.

Compute the ”volume” of the 4-dimensional unit ball, which is the area enclosed by the equation x^2 + y^2 + z^2 + w^2 = 1. Find the range of w and find the w-th cross section (which would be a 3-dimensional solid)

Consider the solid bounded by the paraboloid z=4−x^2−y^2 and the xy-plane. Calculate the volume of this solid.