Math CentralQuandaries & Queries


Question from Chithrabhanu:

If a dom dia is 4.552 and the height is 1.21 what is the surface area?


In my diagram the radius of the base of the dome is $R,$ in your case 4.552/2 units, and H is its height, in your case h = 1.21 units. $B$ is the center of the base of the dome and $C$ is the center of the sphere that forms the dome. The radius of the sphere is $r$ units.


The triangle $ABC$ is a right triangle and hence Pythagoras Theorem insures that

\[R^2 + (R-h)^2 = r^{2}.\]

Since you know $R$ and $h$ you can solve this equation for $r.$

Now use the expression in our response to an earlier question to calculate the surface area.


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