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?

Question

Mathematics

Alejandra Patterson

30 March, 22:57

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?

+1

Answers (1)

Know the Answer?

Laney Smith · Answer 1

First, we determine the volumes of the posts may it be cylindrical in shape or rectangular prism.

(A) cylindrical:

(π (26.7/100) ² - π (24.2/100) ²) * (7.5) = 0.3 m³

(B) rectangular prism:

(40/100) ² (7.5) - (35/100) ² (7.5) = 0.28125 m³

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.