Question

Solid metal support poles in the form of right cylinders are made out of metal with a density of 5 g/cm (cubed)^ 3 . This metal can be purchased for $0.29 per kilogram. Calculate the cost of a utility pole with a radius of 19 cm and a height of 680 cm. Round your answer to the nearest cent.

Answer 1

The cost of the utility pole is $3392.23.

Step-by-step explanation:

To calculate the cost of the utility pole, we first need to find its volume. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Plugging in the values, we get V = π*(19 cm)^2*(680 cm) = 2337504 cm^3. Since the density of the metal is 5 g/cm^3, the mass of the pole is 2337504 cm^3 * 5 g/cm^3 = 11687520 g = 11687.52 kg.

Next, we can calculate the cost of the metal. The cost per kilogram is $0.29. Multiplying the mass of the pole by the cost per kilogram, we get $0.29 * 11687.52 kg = $3392.23. Rounded to the nearest cent, the cost of the utility pole is $3392.23.