Question

A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 2ft and a radius of 5ft. The tank will be made from metal (including its top and bottom). Suppose the total cost of the metal will be 8572.20. How much will the metal cost per square foot? Use 3.14 for pi, and do not round your answer.
Please give an understandable step-by-step explanation. Thank you !!

Answer 1

Answer:

$39 per square foot.

Step-by-step explanation:

The cylinder has a height of 2 feet and a radius of 5 feet.

The total cost of the metal will be (assuming US dollars) $8572.20.

And we want to determine the cost per square foot.

First, we can find the surface area of the cylinder. The surface area for a cylinder is given by the formula:

$SA=2\pi r^2+2\pi rh$

Where r is the radius and h is the height.

Since the radius is 5 feet and the height is 2 feet and using 3.14 for π, the surface area is:

$SA=2(3.14)(5)^2+2(3.14)(5)(2) =219.8\text{ feet}^2$

Therefore, to find the cost of metal per square foot, we can divide the total cost over the amount of surface area. Hence:

$8572.20 / 219.8= \ 39 \text{ per square foot}$

So, the metal costs $39 per square foot.