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The figure shows a rectangular metal sheet measuring 1 m long and 80 cm wide. From each of the four corners of the rectangle a square of side x cm is removed. The remaining part is then folded along the dotted line to form an open cuboid. The metal is 2 mm thick, and its density is 2.5 g/#cm^3#.
a) If A #cm^2# is the area of the unshaded part, show that #A = 8 000 - 4x^2 #
b) Given that the area of the unshaded part is #0.76 m^2#, find the value of x hence state the dimensions of the cuboid.
c) Calculate the mass of the empty cuboid in kg.
d) The cuboid is filled with a liquid whose density is d g/#cm^3#. Given that the mass of the cuboid when full of liquid is 39.8 kg, determine the value of d.