Taper extrude

Hi everyone, hope you are well.
Really new to this. Trying to do a taper hole and struggling to do so. Whenever I try to extrude through something, it simply makes it a cylinder, not with the taper.
I attach two images, the cone I made is in blue. I am trying to use it to make the inside a smooth passageway without hinderance of the two pipes coming in from each side. I hope that makes sense.
Thanks in advance for any assistance.

You can taper when you extrude.

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Thanks very much indeed! I think I was trying to over complicate things.