If a sphere's volume is doubled, what is the corresponding change in its radius?

Volume of a sphere = (4/3) (pi) (radius) ³

The sphere's volume is proportional to the cube of its radius,

so the radius is proportional to the cube-root of the volume.

The only way to double a sphere's volume is to increase

its radius by the factor of

∛2 = 1.26 (rounded).