Step 1 :Let the radius of the sphere be r and the radius of the cone be 3r.
Step 2 :The volume of the sphere is given by the formula: \(V_{sphere} = \frac{4}{3} \pi r^3\)
Step 3 :The volume of the cone is given by the formula: \(V_{cone} = \frac{1}{3} \pi (3r)^2 h\)
Step 4 :Since the volumes are equal, we can set the two formulas equal to each other: \(\frac{4}{3} \pi r^3 = \frac{1}{3} \pi (3r)^2 h\)
Step 5 :Cancel out pi and 1/3 from both sides: \(4r^3 = 9r^2 h\)
Step 6 :Solve for r in terms of h: \(r = \frac{9h}{4}\)
Step 7 :\(\boxed{r = \frac{9h}{4}}\)