We will use the general volume equation for a cylinder which is:

Volume=(pi)(radius)^2(height)

Let 'V' stand for the volume of both cylinders, 'm' stand for the actual height of the cylinder that corresponds to the 9, 'n' stand for the actual height of the cylinder that corresponds to the 4, 'm/n'=9/4, 'x' stand for the radius of of the cylinder that corresponds to the 9, 'y' stand for the radius of the cylinder that corresponds to the 4, and 'x/y' stand for the ratio of the radii. We can write two separate equations with the information given and the volume equation of the cylinder.

V=(pi)(x)^2(m)

V=(pi)(y)^2(n)

Now we will divide the top equation by the bottom one to get:

(V/V)=(pi/pi)(x^2/y^2)(m/n)

Simplifying and plugging in 9/4 for m/n, we get:

1=(x/y)^2(9/4)

Solving for 'x/y', we get:

3/2=x/y

Therefore, the ratio of the radii is 3/2.