Compare two slice directions and translate an axis of rotation

Designer A programs a machine to cut a thin material into the region enclosed by $y=\sqrt{2x-3}$, $2y=x-4$ and the x-axis.

(i) Sketch suitable graphs and find its exact surface area.5 marks

(ii) Rotate that region through four right angles about the x-axis to form a closed object. Find its volume.3 marks

(iii) Designer B rotates the region bounded by $C:y=x^2+3$, $x=4$ and both axes through four right angles about $x=4$. Write the equation of $C$ translated four units in the negative x-direction, and determine the resulting volume.4 marks