Unravelling Surface Area of a Dome

[DaveC426913]

Trying to figure out the answer to another thread.

What is formula for the surface area of a dome?

Googling got me $$2\pi r h$$ (where $$h$$ is the height of the dome above its slice through the sphere). Is that right?

Ultimately, I'm trying to figure out how the area changes as a function of the slice through the sphere. i.e.:

When the slice goes through the centre of the sphere, the area is X (in fact, exactly half of the sphere's area).

OK. Now, if I move the slice out to $$1/2 r$$, what does that do to the area of the dome? Does the area halve? or quarter?

 

[dextercioby]

I advise u draw a picture.Explain the geometry of the drawing.Which is the sphere,which is the paraboloid,is it a revolution paraboloid,are they coaxial,what is "h",what is "r",or simply give the link to the webpage where u got that result.

If you're asking for help,at least do it in a proper way.

Daniel.

 

[DaveC426913]

Guess I didn't get the memo on "the proper way".


(Don't know why this gpt posted twice...)