Question

Solid metal support poles in the form of right cylinders are made out of metal with a density of 6.7 g/cm^3. This metal can be purchased for $0.87 per kilogram. Calculate the cost of a utility pole with a diameter of 18.2 cm and a height of 660 cm. Round your answer to the nearest cent.

Answer 1

The Solution:

Given:

A utility pole with a diameter of 18.2 cm and a height of 660 cm. This means that the pole is a cylinder of the form below:

Step 1:

Find the volume of the utility pole.

By formula,

$\begin{gathered} \text{Volume = }\pi r^2h \\ \text{ in this case,} \\ r=radius=\frac{18.2}{2}=9.1cm \\ h=height=660cm \end{gathered}$

Substituting, we get

$\text{Volume}=\pi\times9.1^2\times660=171702.4898cm^3$

Step 2:

We shall find the mass of the metal used in making the pole.

By formula,

$\begin{gathered} \text{ Density =}\frac{\text{ Mass}}{\text{Volume}} \\ In\text{ this case,} \\ \text{ density=6.7g/}cm^3 \\ \text{Mass}=\text{?} \\ \text{Volume}=171702.4898cm^3 \end{gathered}$

Substituting, we get

$\begin{gathered} 6.7=\frac{\text{ Mass}}{171702.4898} \\ \\ \text{ Mass=6.7}\times171702.4898=1150406.682\text{ grams} \end{gathered}$

Converting to kilogram, we divide by 1000.

$\text{Mass}=\frac{1150406.682}{1000}=1150.406682kg$

Step 3:

Find the cost.

Given that each kilogram cost $0.87, we have the cost as:

$\text{ Cost}=0.87\times1150.406682=1000.8538\approx\text{ \ 1}000.85$

Therefore, the correct answer is $1000.85