Consider a rectangular sheet of solid material of length $l=9 \ cm$ and width $d=4 \ cm$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \ K^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m=0.1 \ kg$ and the specific heat capacity is $C_v=900 \ J \ kg^{-1} K^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \ J$,then the change in area of the rectangular sheet is:

• A
  $2.0 \times 10^{-6} \ m^2$
• B
  $3.0 \times 10^{-7} \ m^2$
• C
  $6.0 \times 10^{-7} \ m^2$
• D
  $4.0 \times 10^{-7} \ m^2$