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.
If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent. The "included angle" in SAS is the angle formed by the two sides of the triangle being used. The "included side" in ASA is the side between the angles being used.
