I’ve never had a geometry class, but am pretty good at figuring these things out. I hope this does not need to exact as I will be rounding to the hundreths and a true circle is round whereas what you are talking about is made from straight pieces:

We know that: Pi R2 = circumference

We know: R = 1/2 Diameter,

So we can say Pi D = circumference

So circumference = 3.1416 x 30 = 94.25

We know the circumference of a semi-circle is half of a circle, so the outside of this semi-circle is 47.125.

You want to use 8 straight pieces to miter together, so 47.125/8 = 5.890625, or 5 57/64.

For ease, round to 5 56/64, or 5 7/8, and you will have a semi-circle with an approximate 29.92 inch diameter.

I’m sure I do not need to say this, but if you want the id to be approx 30, the 5 7/8 needs to be on the mitered length (short side), if you want an approx 30 in od, the unmitered length (long side), needs to be 5 7/8.