# Shapr3D not fulfilling Law of Cavalieri?

**URL:** <https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675>\
**Category:** Modeling Questions\
**Created:** [December 20, 2024, 7:12am UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675 "2024-12-20T07:12:27Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![pgmaker](https://avatars.discourse-cdn.com/v4/letter/p/e495f1/32.png) [@pgmaker](https://discourse.shapr3d.com/u/pgmaker)\
**Post date:** [December 20, 2024, 7:12am UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675/1 "2024-12-20T07:12:27Z")

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hi Community!  
I have been using Shapr3D for education for a while now, I like it really much!

I have one spcific interesting question: In maths class, I wanted to show the law of cavalieri live. It says that the volume of 2 bodies are the same, as long as theyx have the same hight and on every height from buttom to top i can show that the cross sectial area of these bodies are the same.

 ![image](https://us1.discourse-cdn.com/flex002/uploads/shapr3d/original/3X/b/4/b4ecc3d99d9db153e0cb0a8cbd19dce1a9f9a0e9.jpeg)

I created to simple cuboids, one with extrude and one with loft, using the same squre scetch. Of course the measuring tool shows the same volume. However, if i rotate the upper square plane of the lofted cuboid, the volume decreases. If I look at cross section views, I can see that the squares are smaller than the buttom and top square.

I only found this interesting and wanted to ask, if this is just because of how the lofted body is created in the software, or is this an “error”?

Greetings from germany!

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**Author:** ![Lys](https://avatars.discourse-cdn.com/v4/letter/l/67e7ee/32.png) [@Lys](https://discourse.shapr3d.com/u/Lys)\
**Post date:** [December 20, 2024, 12:30pm UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675/2 "2024-12-20T12:30:36Z")

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The decrease in volume when rotating the upper plane of the lofted cuboid is not an error because the lofting tool creates a smooth interpolation between the profiles (in this case, the top and bottom squares). When the top square is rotated, the intermediate cross-sections are no longer simple squares, but skewed quadrilaterals, which reduces their area at certain heights. This results in a smaller overall volume compared to an idealized theoretical scenario where every cross-section is perfectly identical.  
I hope this clarifies things.

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**Author:** ![SCALEMODEL](https://avatars.discourse-cdn.com/v4/letter/s/77aa72/32.png) [@SCALEMODEL](https://discourse.shapr3d.com/u/SCALEMODEL)\
**Post date:** [December 21, 2024, 6:17am UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675/3 "2024-12-21T06:17:11Z")

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![Screenshot 2024-12-20 at 10.15.37 PM](https://us1.discourse-cdn.com/flex002/uploads/shapr3d/original/3X/b/c/bc22b042866d55fdc5c022bb0be0aeb707744ef8.jpeg)

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**Author:** ![pgmaker](https://avatars.discourse-cdn.com/v4/letter/p/e495f1/32.png) [@pgmaker](https://discourse.shapr3d.com/u/pgmaker)\
**Post date:** [December 21, 2024, 6:50am UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675/4 "2024-12-21T06:50:18Z")

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Thanks for the explanation!

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**Author:** ![PEC](https://avatars.discourse-cdn.com/v4/letter/p/67e7ee/32.png) [@PEC](https://discourse.shapr3d.com/u/PEC)\
**Post date:** [December 22, 2024, 10:43am UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675/5 "2024-12-22T10:43:59Z")

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Hi @pgmaker

you can use the revolve tool to create the constant cross section body, and then use history to change the rotation angle.

 ![image](https://us1.discourse-cdn.com/flex002/uploads/shapr3d/original/3X/7/7/77b81a7ec4cf070763c108c591bc55b994e53521.jpeg)

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**Author:** ![SCALEMODEL](https://avatars.discourse-cdn.com/v4/letter/s/77aa72/32.png) [@SCALEMODEL](https://discourse.shapr3d.com/u/SCALEMODEL)\
**Post date:** [December 23, 2024, 12:00am UTC](https://discourse.shapr3d.com/t/shapr3d-not-fulfilling-law-of-cavalieri/35675/6 "2024-12-23T00:00:16Z")

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If you change the units to imperial you won’t get the long 15999.9439.