Question

Solid metal support poles in the form of right cylinders are made out of metal with a density of 6.6 g/cm^3

This metal can be purchased for $0.78 per kilogram. Calculate the cost of a utility pole with a radius of 16.2 cm and a height of 710 cm. Round your answer to the nearest cent. (Note: the diagram is not drawn to scale)

Answer 1

Explanation:

The first step is to calculate the volume of the cylinder:

Volume = π x (radius)^2 x height

Volume = π x (16.2 cm)^2 x 710 cm

Volume ≈ 1.468 x 10^6 cm^3

Next, we can calculate the mass of the metal required to make the pole:

Mass = Density x Volume

Mass = 6.6 g/cm^3 x 1.468 x 10^6 cm^3

Mass ≈ 9.6948 x 10^6 g or 9694.8 kg

Finally, we can calculate the cost of the metal required:

Cost = Price per unit mass x Mass

Cost = $0.78/kg x 9694.8 kg

Cost ≈ $7,561.17

Therefore, the cost of the utility pole would be approximately $7,561.17, rounded to the nearest cent.