Surface area of a dome - Math Central

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Question from Charlie:

Why is the calculation for the surface area of a domed tank less than the surface area of a flat top tank.
Using domed tank formula 2*pi*r(r-(r-dome ht) works out to be less surface area than a flat top tank area formula pi*r x r,
Shouldn't the dome have more surface area than the flat surface ?

Hi Charlie,

The expression you have for the surface area of a dome is correct (except you misses a parenthisis). It is

2 × π r(r - (r - h)) square units

where h is the dome height. This simplifies to

2 × π r × h square units.

dome

If, for example, h = r so that the dome (light blue) is half of the sphere then the surface area of the dome is 2 π r² square units, twice the area ofthe base (dark blue). If h is very small then the area of the cap can be much smaller than the area of the base.

I hope this helps,
Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.