Questions: Electric utility poles in the form of right cylinders are made out of wood that costs 25.99 per cubic foot. Calculate the cost of a utility pole with a radius of 0.5 ft and a height of 25 ft. Round your answer to the nearest cent.

Electric utility poles in the form of right cylinders are made out of wood that costs 25.99 per cubic foot. Calculate the cost of a utility pole with a radius of 0.5 ft and a height of 25 ft. Round your answer to the nearest cent.

Transcript text: Electric utility poles in the form of right cylinders are made out of wood that costs $\$ 25.99$ per cubic foot. Calculate the cost of a utility pole with a radius of 0.5 ft and a height of 25 ft . Round your answer to the nearest cent.

Solution

Solution Steps

Step 1: Calculate the volume of the cylindrical pole

The volume of a cylinder is given by the formula _V_ = π_r_²_h_, where _r_ is the radius and _h_ is the height. In this case, _r_ = 0.5 ft and _h_ = 25 ft.

_V_ = π * (0.5 ft)² * 25 ft _V_ = π * 0.25 ft² * 25 ft _V_ ≈ 19.635 ft³

Step 2: Calculate the cost of the pole

The cost of the wood is $25.99 per cubic foot. Multiply the volume by the cost per cubic foot to find the total cost.

Cost = Volume * Cost per cubic foot Cost = 19.635 ft³ * $25.99/ft³ Cost ≈ $509.55