The line segment with x - and y - intercepts a and b , a ! = 0 , 0 < = y < = b , b > 0 , is revolved about the y - axis to generate a cone. Find its lateral surface area. Furthermore, if the lateral surface and the base forms an angle of 6 0 ◦ and the total area of the cone is 7 5 pi , find the values of a .