Answer
If the hollow sphere is to be modified so that the kinetic energy triples while the mass stays the same, the radius should be increased by a factor of $\sqrt{3}$.
Work Step by Step
The moment of inertia $I=\frac{2}{3}MR^2$ for a hollow sphere of radius R, and the kinetic energy is $KE=\frac{1}{2}I\omega^2=\frac{1}{3} MR^2\omega^2$.
If the sphere is to be modified so that the kinetic energy triples while the mass stays the same, the radius should be increased by a factor of $\sqrt{3}$.
$$KE_{old}=\frac{1}{3} MR_{old}^2\omega^2$$
$$KE_{new}=\frac{1}{3} M(R_{old}\sqrt3)^2\omega^2=3 KE_{old}$$
