Math CentralQuandaries & Queries


Question from Brandon:

I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT?

Hi Brandon,

I drew a diagram of what I think you have.


The radius of the tank is $a = 13$ feet and the height of the tank is $h = 3.5$ feet. You didn't tell us the height $H$ of the tank but I expect it is only the area of the dome that you need. I found an expression for the area of the dome or circular cap on the Wolfram MathWorld web site, that's where I got the notation in my diagram. The expression they have is that the area of the dome is

\[\pi \left(a^2 + h^2 \right) \mbox{ square feet.}\]

For your tank that gives

\[\pi \left(13^2 + 3.5^2 \right) = 569.4 \mbox{ square feet.}\]


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