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Sphere has ring around it. At T=70C the diameter of the sphere is 0.05% larger than the diameter of the ring. At what temp will the ring be able to come off sphere?

Attempt

D_s=1.0005*D_r at 70C

Sphere

delta_V=beta*V_o*delta_T

Ring

delta_L=alpha*L_o*delta_T

L=pi*D_r (circumference)

delta_L=alpha*(pi*D_r,o)*delta_T

Tried relating D_r and D_s with sphere volume eqn (V=4/3*pi*(D_s/2)^3) and circumference of ring eqn C=L_r=pi*D_r and I'm stuck...

Temeperature where D_r=D_s is the point when ring can come off, but I don't know how to get there.