Volume of sphere = 4/3 x (pi)x r^3 .where r is the radius of a circle ..in this case the radius for the smaller circle. and the Volume of the larger one would be 4/3 x (pi)x R^3 . so when they say the volume if the larger one is Twice the smaller one they're bascially telling you that (4/3x(pi)xR^3 = 2 x (4/3x(pi)xr^3)
When you multiply the formula by two you'd get 4/3x(pi)xR^3= 8/3 x (pi)x r^3
Now solve accordingly by taking 4/3 to the other side.. you'll get sth like this
(pi)R^3 = 2(pi)r^3 Cancel the pi out
now you have R^3 = 2r^3 divide the equation now by r^3 R^3/r^3 =2 you can also write this as (R/r)^3 = 2 take the power cube to the other side to get cube root of 2!!! therefore R/r= cube root of 2
