No, I am not mistaken in the title, this is a pencil case!
No need to search for the opening, you can open it anywhere.

Supplies : 9 non-separable zippers
(done with18 cm long zippers but you can choose your size)

Step 1:

Put the zippers side by side, overlapping slightly (if you look closely the edge, there is a 3 mm border, I used it as a guide).

To be sure it doesn't move during sewing, I first overcast the zippers (if they aren't straight the case may take a "spiral" effect that is not very nice).

The longest is changing thread and can colors (I'm a perfectionist, I know ...)..
Don't forget to move the zipper along the way not to interfere with the presser foot.

Step 2:

Zigzag sewing the ends.

Sew the last two zippers to form the tube.

Step 3:

Well, then I'm sorry but we need to do math !!
You learned (yes, yes, it was part of the program):

C = πD (or C = π x 2R)

Clearly, the circumference is equal to π x diameter (or radius 2x x π)

Measure the case circumference and cut circles = π / (C + seam allowance)
(WARNING seam allowance is added to the circumference).

Step 4:

Cut 2 circles in a matching cotton and 2 circles in a stronger fabric (I took a blackout fabric).
I remind you that children always lost pen caps, using a strong fabric prevents from pen holes...

Overlay a cotton circle and a circle of strong fabric and sew zigzag.

Step 5:

Pin a circle on the tube zipper (right sides facing) and sew a straight stitch.
Well here I admit that it is sometimes a bit of a chore not to make fold.

I sew once, I check that everything is well placed and I double (even triple) the seam.

Do the same on the other side (don't forget to open a zipper in order to return the case!!)