blah blah blah ... you lost me
It's not all that hard if taken one step at a time. Hope this helps those who find the maths challenging.
The surface area of a 1) a sphere and 2) a hemisphere. First find the multipliers (using pi = 3.1416)
1) 4 x pi = 12.566
2) 2 x pi = 6.283
These numbers are constant - they don't change for any other examples.
We'll assume that the intention is to produce a hemi-sphere. For a sphere just follow twice over!
Keep the 3 decimals for now. Since we're multiplying, any error will also be multiplied so keeping precision will keep the error small for the moment.
Decide on a desired diameter for the bowl - say 100 (mm!) therefore radius is 50.
From the surface area of a sphere, we need to square the radius - multiply it by itself
3) 50 squared = 50 x 50 = 2500
4) Multiply the results of 2) with the results of 3) to get a surface area -15,708 square millimetres
Decide on a desired finished thickness for the bowl. I'll use 3. We keep units the same - mm here...
From 4) x desired thickness
5) Thickness x surface area = 3 x 15708 = 47,124 cubic millimetres
Suggest that I make the bowl from 5mm sheet so starting with 5mm and hammering out to 3mm.
To get a surface area of our starting circle, divide the volume by our sheet thickness
6) 47,124 / 5 = 9,424.8 square mm
Then to get the dimensions of the circle, use the equation for the area of a circle = pi x r^2 . To start, divide by pi:
7) 9424.8/3.1416 = 3000
The answer to 7) is the radius squared, so to go the other way and find the radius ...
find the square root of 3000
sqrt(3000) = 54.77
Since we've been working all along in mm then we can dispense with the decimals - but round up since you can't hammer what isn't there.
Diameter of 5mm thick circular metal disc = 55mm
This will produce a hemisphere 'about' the desired diameter. By this, the finished bowl (if ideally hemispherical) will be half of the finished thickness (3mm), 1.5mm in - and 1.5mm out from the ideal 100mm design line.
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