Question

Electric utility poles in the form of right cylinders are made out of wood that costs $10.15 per cubic foot. Calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 25 ft. Round your answer to the nearest cent.

Answer 1

Electric utility poles in the form of right cylinders are made out of wood that costs $10.15 per cubic foot.

i.e

$1ft^3=\text{ \ 10.15}$

The electric utility poles are in the form of a cylinder,

To find the volume, V, of a cylinder, the formula is

$\begin{gathered} V=\pi r^2h \\ \text{Where } \\ r\text{ is the radius and h is the height of the cylinder} \end{gathered}$

An electric utility pole with a diameter of 1.5 ft and a height of 25 ft will have a volume of

$\begin{gathered} V=\pi r^2h \\ d=1.5ft \\ r=\frac{d}{2}=\frac{1.5}{2}=0.75ft \\ h=25ft \\ V=\pi\times(0.75)^2\times25 \\ V=44.1786ft^3 \end{gathered}$

Since

$\begin{gathered} if\text{ }1ft^3=\text{ \ 10.15,} \\ 44.1786ft^3=44.1786\times10.15=\text{ \ 448.4}1\text{ (nearest cent)} \end{gathered}$

Hence, the cost of the electric utility pole is $448.41 (nearest cent)