In a design for the Tower of Babel (with an infinite height in order to reach the heavens), the horizontal cross-sections are circles, with the radius as a function of height given by the equation: \[ r=f(h)=\frac{h}{\left(h^{3}+a ight)} \] (a) If there is 4 cubic kilometres of material available for the construction of the tower, find the value that the parameter a must take. (b) The number of days per kilometre of height d that it takes to build a section of the tower depends on the cross-sectional area and the steepness of the sides, according to the function: \[ d=g(h)=\frac{\pi f(h)^{2}}{-f^{\prime}(h)} .\] Find an explicit expression for this function. (c) Use the function d = g(h) to find the time it would take to build the entire tower, if it exists.