square meter of dome?

[ilikethai]

please help if a dome roof is on a flat surface.  if the distance around the base of a dome (circumference) is 100 meters and the height to the center top is 58 meters what is the area in square meter?  thankyou in advance. :)

Edited March 14, 2021 by ilikethai

[blackcab]

1,591.54943 m²

Assuming your dome is a hemisphere...

However, given the somewhat strange proportions of your dome I cannot rule out that you are describing a spherical dome. If you are, the answer would be significantly different.

Consider that your dome's base has a diameter of 31.8309 meters, but it is 58 meters high...

It might help if you draw the outline of the dome and the base, take a picture and upload it.

[Jan Dietz]

If the Circumference is 100m, divide by Pi to get the Radius, so R = 31.8m

Surface = Pi * R^2 so 3175m^2

Height doesn't matter, unless you want to calculate standing room only...

[JAS21]

I agree with Mr Blackcab   2*Pi*r*h  1591 and a bit M2

[VocalNeal]

I believe it to be a paraboloid.

 

So the answer according to https://www.vcalc.com/wiki/vCalc/Paraboloid+-+Surface+Area

at d= 31.8309 and H= 58 the answer is 11646.29977411767

Taking it to 2 decimal places ie. 31.83 to the nearest centimetre would be 11645.84

at 4 am not being able to sleep my brain hurts????

[Crossy]

Someone got the contract to glaze this??

[Elad]

With a height of 58 m then the dome would be half a 'prolate spheroid'

Where a = 15.915 m and c = 58 m

The formula for the surface area is:

Plugging in the numbers for the area and dividing by 2 I get 4694 sqm

[VocalNeal]

1 hour ago, VocalNeal said:

I believe it to be a paraboloid.

 

So the answer according to https://www.vcalc.com/wiki/vCalc/Paraboloid+-+Surface+Area

at d= 31.8309 and H= 58 the answer is 11646.29977411767

Taking it to 2 decimal places ie. 31.83 to the nearest centimetre would be 11645.84

at 4 am not being able to sleep my brain hurts????

Well I've done this before trusting others calculations. ????

At 100m circumference the Diameter is as above 15.91m and not 31.83.

so again using  

https://www.vcalc.com/wiki/vCalc/Paraboloid+-+Surface+Area

 

we get 4769.16 sq m 

So somewhere between 4694 and 4769

[bankruatsteve]

2 minutes ago, VocalNeal said:

At 100m circumference the Diameter is as above 15.91m and not 31.83.

The diameter is 31.83.  The radius is 15.91.

[VocalNeal]

16 minutes ago, bankruatsteve said:

The diameter is 31.83.  The radius is 15.91.

It is to early for me. 555 Never post when sleepy. So I was wrong for inputting diameter instead of radius. 

Comes from not committing the thing to paper first?

I'll stick to the jokes forum!

Edited March 14, 2021 by VocalNeal

[ilikethai]

thankyou everyone.  even after reading the replies..my brain really hurts and still confused.  I'm not a math person every time I study math I shake and sweat. don't worry I still got some more math question coming this afternoon.

update: here's my pic. please help on finding sq meter of the dome

Edited March 15, 2021 by ilikethai

[blackcab]

The picture you have drawn is a hemisphere, however the measurements you have given will not result in a hemispherical shape.

This is because your base is much narrower than the height of the building.

If you want a domed shape then either your base has to be wider or your height has to be lower, otherwise you will end up with either a. a very pointy-shaped dome or b. something like Crossy pictured above.

If your base cannot change one option is to create a true hemisphere with a circumference of 100 meters then sit it on a vertical stem wall to gain the extra height.

Remember that just because you can draw it, it doesn't mean that it can be built.

[ilikethai]

blackcab, what is the base is 200m around?

[bankruatsteve]

1 hour ago, ilikethai said:

here's my pic. please help on finding sq meter of the dome

With a base circumference of 100m, the radius of a hemisphere would be 15.92m.  An apex of 58m would look more like a cucumber.  A hemisphere with radius of 58m would have a base circumference of 364m

[bankruatsteve]

To visualize what you are giving as dimensions, measure the diameter of your picture.  Looks like about 40mm.  Then multiply that by 1.8.  If the diameter measures 40mm that would be about 73mm.  So put a dot 73mm above the center of your picture and make a curve to that.   

The surface area would be about what Elad posted above.

Edited March 15, 2021 by bankruatsteve
Got stuck on radius dimension.

[blackcab]

1 hour ago, ilikethai said:

blackcab, what is the base is 200m around?

 

I have no idea what you are asking.

[gamb00ler]

Perhaps the OP wishes to have a spherical cap (https://en.wikipedia.org/wiki/Spherical_cap) not a hemispere or paraboloid.

The Wiki link gives the mathematical formulae required for calculating the surface area.

I think OP made an error in giving the height he wishes to use.

 

Given a (radius of the cap base) which is 15.91m and h (height of the cap peak) is 58m.

Area = π (a² + h²) = 3.14 * 3617.13 = 11,358m².

To find the radius of the entire sphere solve this equation for r:

2π*r*h = π (a² + h²)   or  r = (a² + h²)/(2*h) = 3617.13/116 = 31.18m

The object described looks like Crossy's posted image.

 

Edited March 15, 2021 by gamb00ler

[blackcab]

To put this into a real world perspective, if you want a dome that is 58 meters high then you will need a big budget.

The actual dome of the Millennium Dome in the UK is 52 meters high in the middle:

 

The new tower in Roi Et is 101 meters tall:

 

If your dome is a hemisphere and it has a height of 58 meters and a circumference of 364 meters, as noted by Charlie, the land covered would be 10,568 m² or slightly larger than one hectare, or approximately 6.6 rai.

[gamb00ler]

1 hour ago, ilikethai said:

blackcab, what is the base is 200m around?

assuming you mean "what if the base is 200m around?" and you want a spherical cap:

Then the surface area  would be 13,751.22m²

[ilikethai]

ok, I'm so sorry for this long tread.  I should just had explain better.  Sorry for my bad English.  Anyway what I'm trying to achieve is total area of land with a big mound.  how would I achieve this? 

I made a basic map for ease of calculation.  It's possible to find out sqm (area) even if a land is not a square shape?  I want to hire people to clear out the woods to make a farm.  The people want me to measure as accurate as possible the total land and including the mound.

[PGSan]

If the lengths between your resits are accurate then the shape is definitely wrong.  This makes it impossible to give anything like a good estimate of what the area may be.  (The extra area from the mound not being flat probably makes little proportional difference to this estimate.)

Edited March 16, 2021 by PGSan

[blackcab]

Use the free measuring tools on Google Maps. Ignore the curvature of the hill and measure everything as if it were flat.

[ilikethai]

5 hours ago, PGSan said:

If the lengths between your resits are accurate then the shape is definitely wrong.  This makes it impossible to give anything like a good estimate of what the area may be.  (The extra area from the mound not being flat probably makes little proportional difference to this estimate.)

the drawing lengths are drawn to make things easier to calculate. my question is is it even possible to calculate manually even if the lengths are not square or rectangle shape?  can I add all those lengths up and make them into 4 sides and multiple side A by side B?

[blackcab]

17 minutes ago, ilikethai said:

my question is is it even possible to calculate manually even if the lengths are not square or rectangle shape?

 

Yes, if you are a surveyor. Surveyors do this all the time, although nowadays they use a computer. If you have accurate measurements it is possible to do this by hand, but why are you trying to make your life so very complicated?

You can have the whole job finished in about 5 minutes with Google maps. The measurements below took me about 2 minutes to do. For reference, the area I measured is the island in the middle of Lumphini Park in Bangkok.

As you can see, the area of the island is 16,162.51 m².

[treetops]

Your drawing gives the dome height as 10m but the OP says 58m.  Which is it?

It seems to me that it could be described as a spherical cap and surface area calculation can be seen here.  Get the over all measurements from Google as described and add on the surface area of the cap minus the surface area of a 100m circumference circle, or just type the numbers in here:

http://www.ambrsoft.com/TrigoCalc/Sphere/Cap/SphereCap.htm#cap