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Please bear with me, I am new to this software and 3D in general.

I currently have a shape consisting of a cylinder and a sphere embedded in the top of the cylinder: 3D model consisting of a cylinder and a sphere

I am looking to create a curve that extends from the bottom half of the sphere and gently curves outward until reaching the cylinder's full width. I have drawn an example of what I want in MS Paint (it's a bit shaky but it's clear where it needs to be):Drawing of the aforementioned desired shape provided as an example

I have been playing around with the bevel tool, and while increasing the amount of segments does smooth out the curve, there is always a defined edge where the bevel stops:Diagram showing how the bevelling of the edge suddenly stops

I am looking to somehow get rid of this edge and create a smooth, even shape that slowly curves outward to the full width of the cylinder. I have been unable to find any solutions to this problem on both Google and this website.

I have seen similar posts where the solution was to apply the scale; I have already done that with both shapes.

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Welcome to BSE,

Here is what I would suggest:

(Optional): In Object mode, select both your cylinder and your sphere (Shift+Left Click). Use CTRL+J to join your meshes into a single object. Although not required, you might find this makes your model easier to work on.

Select your cylinder and press Tab to enter Edit Mode

enter image description here

Use CTRL+R to add a loop-cut to the cylinder:

enter image description here

Rotate your view and select the top face: Make sure you are in Face Select mode. The shortcut is 3 on the Number row of your keyboard (not the Number pad):

enter image description here

enter image description here

Use S to scale the face down. After press S you can also use the Numpad to enter a specific scale (i.e 0.5):

enter image description here

Now we want to bevel the edge loop in the center of the cylinder. First we need select it. The easiest way to do this is by using Alt-Select:

  • Make sure you are in Edge Select mode. The shortcut is 2 on the Number row of your keyboard (not the Number pad):

enter image description here

  • Hold Alt and Left-Click on one of the edges in the loop that we want to bevel:

enter image description here

You can now bevel as before, and hopefully get the result you are looking for.

enter image description here

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