Initial Knowledge Check Question 20 Mailen 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 $\$ 18,408,15$. 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. I Don't Know Submit
Solution
Step 1 ：The given diameter of the cylinder is 12 m. The radius of the cylinder is half of the diameter, so it is \(6 \, m\).
Step 2 ：The height of the cylinder is given as \(8 \, m\).
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 \(527.79 \, m^2\).
Step 7 ：Dividing the total cost by the surface area, we get the cost per square meter as approximately \$34.88.
Step 8 ：\(\boxed{\text{The cost of the steel per square meter is approximately \$34.88.}}\)
