How can I get a different color in the white area of the "flower petals", than what I put in the background, inside the circle?

If I select the circle, and put in a fill color, the white area of the "petals" gets the same color.
The only thing I can think, is to make a copy of the "flower" shape (without the holes), make it white, and put it underneath, between the filled circle and the "flower". Is that the best way?
What if I wanted to put a different color in the white area of each "petal"? Would I make a copy of the "flower" (without holes), make each "petal" a different color, and put it between the "flower" and the filled circle?
Any help appreciated, as always, from ye wise Inkscape folks

is made for things like this.
or Live Path Effects in 0.46, then edit the file in 0.44 and then go back again to 0.46 you may find you can't edit that object the same way again (all the smarts may be lost). Other tools like
will be fine though. Just be aware that you may loose some effect so you might like to keep a backup.