math

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 aluminum. The city can choose to buy the posts shaped like cylinders or

the posts shaped like rectangular prisms.

The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of

53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a

square base that measures 40 cm on each side.

The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.

a) What is the cost of the cylindrical posts, to the nearest cent?

b) What is the cost of the rectangular-prism posts, to the nearest cent?

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  1. cylinder: π/4 * (53.4^2 - (53.4-5)^2) * 750 cm^3 * 2.7 g/cm^3 * 1kg/1000g * $0.38/kg = $307.62
    prism: (40-5)^2 * 750 cm^3 * 2.7 g/cm^3 * 1kg/1000g * $0.38/kg = $942.64

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    oobleck

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