Initial Knowledge Check
Question 20
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A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of $8\mathrm{m}$ and a diameter of $12\mathrm{m}$. The container will be made from steel (including its top and bottom). Suppose the total cost of the steel will be $\mathrm{\$}18,408,15$. How much will the steel cost per square meter?

If necessary, refer to the list of geometry formulas.
For your calculations, do not round any intermediate steps, and use the $\pi$ button on the ALEKS calculator. Round your answer to the nearest cent.
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Step 1 ：The given diameter of the cylinder is 12 m. The radius of the cylinder is half of the diameter, so it is $6m$.

Step 2 ：The height of the cylinder is given as $8m$.

Step 3 ：We can substitute these values into the formula for the surface area of a cylinder, which is $2\pi r(h+r)$, to find the total surface area.

Step 4 ：The total cost of the steel is given as $18,408.15.

Step 5 ：We can then divide the total cost of the steel by the total surface area to find the cost per square meter.

Step 6 ：By substituting the values into the formula, we get the surface area as approximately $527.79m^2$.

Step 7 ：Dividing the total cost by the surface area, we get the cost per square meter as approximately $34.88.

Step 8 ：$\boxed{{\displaystyle \text{The cost of the steel per square meter is approximately \$34.88.}}}$