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  4. What is the 3D shape with the maximum surface area?
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What is the 3D shape with the maximum surface area?

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Offline scientizscht (OP)

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What is the 3D shape with the maximum surface area?
« on: 26/08/2020 17:28:39 »
Hello

Two cylinders with the same volume but different radius, have the same surface area?

If not, how much is the difference between two 5mL cylinders with radius 10mm and 1mm?
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Offline Bored chemist

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Re: What is the 3D shape with the maximum surface area?
« Reply #1 on: 26/08/2020 17:54:20 »
Quote from: scientizscht on 26/08/2020 17:28:39
Two cylinders with the same volume but different radius, have the same surface area?
No

Quote from: scientizscht on 26/08/2020 17:28:39
If not, how much is the difference between two 5mL cylinders with radius 10mm and 1mm?
What did  your last slave die of?

Incidentally,
"What is the 3D shape with the maximum surface area?"
This sort of thing.
https://en.wikipedia.org/wiki/Menger_sponge#Similar_fractals
« Last Edit: 26/08/2020 17:58:48 by Bored chemist »
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Offline chiralSPO

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Re: What is the 3D shape with the maximum surface area?
« Reply #2 on: 26/08/2020 19:14:36 »
It's quite easy to find the surface area of a cylinder:

the top and bottom circle are the same, each having area: b3135cacbb8ef8baa45b182bd0fbd78a.gif where r is the radius of the cylinder

and the outside is just 575cf003beaec872b5de31b5e36a2918.gif where h is the height of the cylinder
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Offline CPT ArkAngel

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Re: What is the 3D shape with the maximum surface area?
« Reply #3 on: 26/08/2020 21:45:54 »
What is the best design for a heatsink?
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Offline evan_au

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Re: What is the 3D shape with the maximum surface area?
« Reply #4 on: 27/08/2020 08:58:49 »
This one: https://en.wikipedia.org/wiki/Heat_pipe

Of course, that only defers the problem, as the heat pipe needs a cold sink...
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Offline alancalverd

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Re: What is the 3D shape with the maximum surface area?
« Reply #5 on: 27/08/2020 11:06:08 »
There is no single best design. The optimum design depends on the nature of the heat loading, the specified temperature excursion limits of the source, the nature and availability of the cold source, and a whole load of other considerations. Liquid sodium is an excellent conductor in exhaust valves and nuclear reactors, but isn't everyone's cup of tea.
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