Consider the region bounded by the y-axis, y = 12,  and  y = 1 + 8x3/2. (a) Write, but do not evaluate, an integral equation that will find the value of k so that  x = k  divides the region into two parts of equal area. (Round your answer for the upper limit of the integral to two decimal places.)   (c) The region is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are rectangles with a height of 3 times that of its width. Find the volume of this solid. (Round your answer to three decimal places.)

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