Hi @ingeniousosprey!
Wow, thank you! You are right: there should be a cubed instead of squared. You are very attentive, well done! Keep it up. 🙂
It is possible to solve this problem without trying the multiple-choice answers, but you will need to use a cube root and volume formula to do it.
Here: $$3=\frac{V_2}{V_1}=\frac{(^4/_3)\times\pi\times (r_2)^3}{(^4/_3)\times\pi\times (r_1)^3}=\frac{(r_2)^3}{(4.5)^3}$$ $$(r_2)^3 =3\times (4.5)^3$$ $$r_2 = \sqrt[\bf 3]{3\times (4.5)^3} = 4.5\times\sqrt[\bf 3]{3}$$ $$d_2 = 2\times r_2=9\times\sqrt[\bf 3]{3}={\color{blue}12.980...}\approx \boxed{\color{blue}13}.$$
