A leak proof cylinder of length 1m, made of a metal which has very...

According to Archemedes Principle, weight of the body is balanced by the upward thrust force due to buoyancy.

At $0 ° C$, $mg = A ( 100 - 20 ) {ρ}_{0 ° C}g$, where $A$ is area of cross-section of cylinder and ${ρ}_{0 ° C}$ is density of water at $0 ° C$.
At $4 ° C$, $mg = A ( 100 - 21 ) {ρ}_{4 ° C}g$, where ${ρ}_{4 ° C}$ is density of water at $4 ° C$.
$\dfrac{{ρ}_{4 ° C}}{{ρ}_{0 ° C}} = \dfrac{80}{79} = 1.01$