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=(18.2)/(2)=9.1cm \\ h=height=660cm \end{gathered}`

Substituting, we get

`\text{Volume}=\pi*9.1^2*660=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}*171702.4898=1150406.682\text{ grams} \end{gathered}`

Converting to kilogram, we divide by 1000.

`\text{Mass}=(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*1150.406682=1000.8538\approx\text{ \$1}000.85`

Therefore, the correct answer is $1000.85