Question

solid metal support poles in the form of right cylinders are made out of metal with a density of 7.6 g/cm³. this metal can be purchased for $0.51 per kilogram. calculate the cost of a utility pole with a radius of 20.5 cm and a height of 620 cm. round your answer to the nearest cent. (note: the diagram is not drawn to scale)

Explanation:

Step1: Calculate the volume of the cylinder

The formula for the volume \( V \) of a cylinder is \( V=\pi r^{2}h \), where \( r = 20.5\space\text{cm} \) and \( h=620\space\text{cm} \).

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Step2: Calculate the mass of the metal pole

Density \(
ho = 7.6\space\text{g/cm}^3 \), and mass \( m=
ho\times V \).

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Convert grams to kilograms: \( 6221188.392\space\text{g}=\frac{6221188.392}{1000}=6221.188392\space\text{kg} \)

Step3: Calculate the cost of the metal pole

The cost per kilogram is \( \$0.51 \), so the total cost \( C = 0.51\times6221.188392 \)

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Round to the nearest cent: \( \$3172.81 \)

Answer:

\(\$3172.81\)