New streetlights will be installed along a section of the highway. the posts for the streetlights will be 7.5 m tall and made of aluminium. the city can choose to buy the posts shaped like rectangular prisms. the cylindrical posts have a hollow core, with aluminium 2.5 cm thick, and an outer diameter of 53.4 cm. the rectangular-prism posts have a hollow core, with aluminium 2.5 cm thick, and a square base that measures 40 cm on each side.
the density of aluminium is 2.7 g/cm³, and the cost of aluminium is $0.38 per kilogram.
part a: if all posts must be the same shape, which post design will cost the town less?
part b: how much money will be saved per streetlight post design will cost the town less?