1. the base of a solid is a quadrant of a circle of radius a. each cross section perpendicular to one edge of the base is a semicircle whose diameter lies in the base. find the volume.

2. find the volume of the solid of revolution generated when the area bounded by the curve y = x, y=0, and x=4 is revolved around i) the x-axis and ii) the y-axis.

3. a hole of radius sqrt(3) is bored through the center of a sphere of radius 2. find the volume removed.

4. find the volume of the solid generated by revolving the region enclosed by the graphs of y =e^(−x^2), y =0 , x =0 , and x =1 about the y-axis.

5. find the length of the curve given by y = (1/3)x^3 + 1/(4x), from x=1 to x=3.