Question

Electric utility poles in the form of right cylinders are made out of wood that costs $12.62 per cubic foot. Calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 45 ft. Round your answer to the nearest cent.

Answer 1

To find the cost of a wooden utility pole, first calculate the pole's volume using the formula for the volume of a cylinder, then multiply by the cost per cubic foot of the wood. The total cost for a pole of 1.5 ft diameter and 45 ft height is approximately $1004.47.

Step-by-step explanation:

To calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 45 ft, we will use the volume formula for a cylinder: V = πr^2h, where V is the volume, r is the radius, which is half the diameter, and h is the height of the cylinder. The cost of the wood per cubic foot is given as $12.62.

First, calculate the radius of the pole: radius = diameter / 2 = 1.5 ft / 2 = 0.75 ft.

Calculate the pole's volume: V = π(0.75 ft)^2(45 ft).

Now, calculate the total cost:

1. Find the volume of the pole: V = π(0.75)^2(45) ≈ 79.57 cubic feet.
2. Calculate the cost: total cost = volume × cost per cubic foot
3. So, total cost = 79.57 cubic feet × $12.62/cubic foot ≈ $1004.47.

Therefore, the cost of a wood utility pole with a diameter of 1.5 ft and a height of 45 ft is approximately $1004.47, rounded to the nearest cent.