The diameter of a metal ring is 'D'  and coefficient of linear expansion is  α, if the temperature of the ring is increases by 10C , The circumference of the ring will increase by  xπDα where  x=

circumference of ring is S=2πR=2πD2 S=πD differentiate ΔS=πΔD             coefficient of linear expansion α=ΔDDΔt⇒ΔD=DαΔt;ΔS=xπDα ; substitute in above equation  xπDα=πDαΔt x=Δt    given Δt   =1 ⇒x=1