If anyone could explain how this problem is done, it would be very much appreciated!
Write the equation for the surface generated by revolving the given around the indicated axis.
4x + 9y^2 = 36 around the y-axis
where r is the radius of the circle in the cross-section, which will depend on the value of y we choose for the cross-section. The radius will be equal to the distance from the point on the surface to the y-axis, which in this case will be measured by the x value. Thus the radius is given by the original equation:
and the surface becomes: