Deleting parts of an object located at the interior of another object, after executing 'intersect faces with model'

I was able to successfully recreate the wood thread insert pictured below.

The 2nd image, shows what the interior of the cone looked like, after executing ‘intersect faces with model’, there are 14 different cubic shapes need to be deleted. Would there be a quicker alternative than using the eraser tool, to remove these faces at the interior?

Skp: 039_thread insert.skp (2.5 MB)

You can use the solid tools for this (Make/PRO)…
(Sorry for the German gif)

solid

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‘Outershell’ is in the web versions as well as Pro…

john

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After doing intersect faces with model, I highlight the entire object, and click the outer shell icon.

I get the message:

One or more of the selected objects is either not a solid or is locked. The non-solid/locked objects will be de-selected before this operation is performed.

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I’ve never been able to use the outer shell tool either for this very reason. My object, no matter how tight it seems to be, is never a solid or is always locked. : (

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For outer shell to work all the geometry must be solid groups or components, no raw geometry or non solids. So no intersecting before doing outer shell is needed.
Here you see I have simply positioned the blocks into the truncated cone, no intersecting, then run outer shell.
Outer%20shell

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