This applet illustrates the solid of revolution when the region bounded by the y-axis, y = 4, and [math]f(x)=x^2[/math] is revolved about the y-axis. Options are given to display the solid of revolution and/or the approximating disk and/or the approximating shell.

[list][br][*]Write an expression that gives the volume of an approximating disk.[br][*]Write an integral that represents the volume of the solid of revolution using the method of disks (circular cross sections).[br][*]Write an expression that gives the volume of an approximating shell.[br][*]Write an integral that represents the volume of the solid of revolution using the method of shells.[br][/list]