Let's call the radius of the circle "r". The formula for the area of a sector of a circle is given by:
(θ/360) * π * r^2,
where θ is the central angle of the sector in degrees.
In this case, we know that the central angle is 315° and the area of the sector is 504π, so we can set up an equation as follows:
(315/360) * π * r^2 = 504π
Solving for r, we can isolate it on one side of the equation:
r^2 = 504 / (π * (315/360))
To simplify the expression on the right-hand side, we can divide both the numerator and denominator by 45 (which is a factor of both 315 and 360):
r^2 = 504 / (π * (7/8))
Finally, taking the square root of both sides gives us:
r = sqrt(504 / (π * (7/8)))
So the radius of the circle is approximately 17.14 inches.