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I want to calculate volume of region between the cylinders x^2+y^2=36 and x^2+z^2=36. How can I code it in mathematica? and there is also another question form like this one. enter image description here

I wanna calculate this also. Thanks.

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  • $\begingroup$ I dont think so because when I put my functions there, I get several errors :( $\endgroup$ Jun 11, 2023 at 21:35
  • $\begingroup$ Please include in your question the code you are using. $\endgroup$
    – bbgodfrey
    Jun 11, 2023 at 23:20
  • $\begingroup$ Volume@{ImplicitRegion[{x^2 + y^2 <= 49, z >= 0, x + z <= 4}, {x, y, z}], ImplicitRegion[{x^2 + y^2 <= 49, z <= 0, x + z >= 4}, {x, y, z}]} $\endgroup$
    – cvgmt
    Jun 12, 2023 at 0:25
  • $\begingroup$ ImplicitRegion[{x^2 + y^2 <= 36, x^2 + z^2 <= 36}, {x, y, z}] // Volume $\endgroup$
    – cvgmt
    Jun 12, 2023 at 0:26

1 Answer 1

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Try

reg = ImplicitRegion[{x^2 + y^2 <= 49, z >= 0, x + z <= 4}, {x, y, z}]
Volume[reg]
(*2 (19 Sqrt[33] + 49 \[Pi] + 98 ArcSin[4/7])*)

Hope it helps!

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  • $\begingroup$ This output scared to me. Is there anyway to convert this like 144π or 500π? $\endgroup$ Jun 11, 2023 at 21:39
  • $\begingroup$ Obviously the result isn't a product of Pi with some number! $\endgroup$ Jun 11, 2023 at 21:44

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