Question

Solid metal support poles in the form of right cylinders

are made out of metal with a density of 7.8 g/cm³. This
metal can be purchased for $0.61 per kilogram.
Calculate the cost of a utility pole with a radius of 11.7
cm and a height of 670 cm. Round your answer to the
nearest cent.

Answer 1

$1370.94

Explanation:

First, calculate the area of the base using the formula:

area of a circle = πr² (let me know if you need more details regarding this)

area of a circle = π x 11.7²

area of a circle = 430.05 cm²

Then multiply this by the length of the pole (670 cm) to find the total cm cubed in the pole.

430.05 x 670 = 288133.5 cm³

The density of the metal is 7.8 g/cm³, so to calculate how many grams. of the metal, we need to multiply the cm³ (288133.5) by 7.8

288133.5 x 7.8 = 2247441.3 grams of metal.

as the price of the metal is measured in kilograms we can convert the grams of metal we need into kilograms by dividing by 1000.

2247441.3 ÷ 1000 = 2247.4413 kilograms.

we're told the metal costs $0.61 per kilogram so we can multiply the total kilograms (2247.44) by 0.61

2247.44 x 0.61 = 1370.94

∴ the metal for the pole will cost $1370.94