Start with the formula for the vol. of a cyl.: Vc = pi*r^2*h.
Here, V = 692.37 in^3 = pi*(r^2)(4.5 in). Divide both sides by 4.5*pi to obtain r^2, and then find the sqrt of the result:
692.37 in^3
----------------- = 48.98 in^2. The radius is sqrt(48.98 in^2) = 7 inches.
4.5(3.14)
Check: Vc = pi*r^2*h = pi*(7)^2(4.5) = 692.72 in^3. Close enough!