a company is going to make an oil container in the shape of a cylinder. as shown below, the container will…

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 6 m and a radius of 4 m. the container will be made from steel (including its top and bottom). if the steel costs $23 for each square meter, how much will the steel cost in total? use 3.14 for $\\pi$, and do not round your answer.

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 6 m and a radius of 4 m. the container will be made from steel (including its top and bottom). if the steel costs $23 for each square meter, how much will the steel cost in total? use 3.14 for $\\pi$, and do not round your answer.

Answer

Explanation:

Step 1: Identify the formula for the surface area of a cylinder.

The total surface area $A$ of a cylinder with radius $r$ and height $h$ is given by $A = 2\pi r^2 + 2\pi rh$.

Step 2: Substitute the given values into the formula.

Given $r = 4$, $h = 6$, and $\pi = 3.14$: $A = 2(3.14)(4^2) + 2(3.14)(4)(6)$ $A = 2(3.14)(16) + 2(3.14)(24)$ $A = 100.48 + 150.72 = 251.04 \text{ m}^2$

Step 3: Calculate the total cost.

Multiply the surface area by the cost per square meter ($23): $\text{Total Cost} = 251.04 \times 23$ $\text{Total Cost} = 5773.92$

Answer:

$5773.92