Above is a basketball cake. 8" in diameter. The base of the spherical cakes I am envisioning would be higher up than the bottom of the cake above and would serve as a much wider support. Approximately 40% of the way down from the diameter at its widest.
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Consider these:
Kundalini 10inch Ball Cake Pan Ball Cake Pan Aluminum 3D 10inch Sports Ball Cake Pan DIY Birthday Cake Pan https://a.co/d/dxcGoCc
There are a number of different sizes, so, with proper aluminum supports and weighting, a smaller diameter bowl could be nested inside a larger one and the space in between filled with batter.
Alternatively, you could use stainless steel or glass oven proof mixing bowels. Here is a YouTube video on this approach:
https://youtu.be/atTbY3oosuM?si=OjwuQz__A9DDbbM3
Read the comments as special precautions are needed to ensure the center of the half sphere bakes through. Of course, your cake diameter would be determined by the size of the bowl and here is a set of 12 12-inch stainless steel bowls that might work:
Pinkunn Set of 12 Stainless Steel Mixing Bowls Bulk Nesting Metal Salad Bowls Food Mixing Bowls Baking Prep Reusable Large Bowl for Kitchen Restaurant Home Cooking, Silver (11.8 x 3.74 Inch) https://a.co/d/a9B8qYh
Here it is in ovenproof Pyrex glass:
Pyrex Prepware 4-Quart Rimmed Glass Mixing Bowl, Clear https://a.co/d/1ZbyohC
Good Luck!