The height of a cylinder is 4.5 inches and the volume is 692.37 in what is the radius

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!