If radius of earth were increased by a factor of 3, by what factor would its density have to be changed to keep the value of ‘g’ same.

the formula for calculating the density of the earth is given as

ρ = M /V = [gR² / G] / [(4/3)πR³]

as g = GM/R² and V = (4/3)πR³

so,

ρ = (3/4).(g / πRG)

now, if the radius is increased, the new density will be given as

ρ' = (3/4).(g / πR'G)

now as

R' = 3R

so,

ρ' = (3/4).(g / π(3R)G)

so,

ρ' = (1/3).(3/4).(g / πRG)

thus, 

ρ' = (1/3)ρ

so, the new density would decrease to one-third its initial value.