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?
Then, we calculate for the amount of substance (A) cylindrical: (0.3 m³)(2700 kg/m³) = 810 kg (B) rectangular prism : (0.28125 m³)(2700 kg/m³) = 759.375 kg
Then, calculate for the costs (A) (810 kg)($0.38/kg) = $307.8 (B) (759.375 kg)($0.38/kg) = $288.56
Thus, the answer for A is rectangular post B. About $19.24 can be saved.
