Surface area of a cylinder question

[Asphyxiated]

1. The problem statement, all variables and given/known data

This is actually for my Physics 211 class but the question is very simple. We were asked to construct a cylindrical space station to specific parameters which are not important to the question. I know that my cylinder has a radius of 399.97m and a rotational period of 40.12 seconds to fit the given requirements. It also states that the space station must have a surface area equal to .8 km^2 or 800 m^2. The surface area of a cylinder (minus the top and the bottom which we are to ignore) is:

2 \pi r h = A

That is:

2 \pi (399.97) h = 800 m^{2}

h = \frac {800 m^{2}}{2 \pi (399.97)} = .318 m

which is only about a foot.... Am I looking at this wrong is is the height seriously suppose to be .318 meters? Is the 800 suppose to be squared as well by chance? lol cause if it was i get a height of 254.66 m which sounds a whole lot better to me.

Please note that I know that the other numbers I am using are 100% correct, i have confirmed the with my teacher, i just never thought to ask about the height but it turns out I squared 800 before and got the more reasonable (to me) 254.66 meters.... Now that I am writing the lab it seems that it should just be 800 and now the height is only .318m! lol, let me know what you think.

Thanks!

[SteamKing]

Asphyxiated: Remember 1km = 1000 m, therefore 1 km^2 = 1 square km
1 km^2 = 1000 m x 1000 m

The SA of the station is then 0.8 km^2 = 800000 sq. m

[Mentallic]

Is the 800 suppose to be squared as well by chance?

Yep :wink:

1km2=10002m2=1,000,000m2

edit: sorry I mistakenly wrote 800,000 when I was meant to write 800^2=640,000

[Asphyxiated]

Ok good lol, I am not sure why I was second guessing myself the first time. Thanks for clearing that issue up. I think studying for my calc II finals have thrown me off on my physics stuff.

Thanks much though!