Find the volume of the solid generated by revolving the line around the x-axis, where .
This is a cone with radius 4 and height of 4. Since the volume of a cone is given by the formula , we should get a volume of . Our axis of revolution is the x-axis so our radius function is a function of x. Moreover, it is since the distance from our axis of revolution to the function is always x. Thus, the volume is given by