To find the new volume, we will substitute the new radius (18r) into the volume formula:
V’ = (4/3) * π * (18r)^3
By simplifying this equation, we get:
V’ = (4/3) * π * 5832r^3
This shows that the new volume, V’, is 5832 times the original volume, V. Therefore, when the radius is multiplied by 18, the volume of the sphere increases by a factor of 5832.