Maybe like this
A Blend Method (I don't know what is exactly needing)
Cylinder has not upCaps , Box has not bottom cap
Make one - Blend Perimeter Cylinder to Rectangular Box - Join for have a solid - (Left one) and Duplicate
As they are independant & Solid you can bring closer them for a more intricated result :)
Boolean Union :)
Here the independants

Here the Union moved if necessary (it's a solid )
All takes 10 seconds :)
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