Does induced EMF depend on volume?

If I place two sheets in a uniform magnetic field, one very thick and one very thin (i.e. one with large volume and one with small volume) so that the flux is at normal incidence to the sheets, would the EMF be larger in the thicker sheet? I ask because the only equation I can find to calculate EMF is that it is equal to -1*d(flux)/dt and this has no dependance on volume, only the area of the sheet cutting the flux lines. What do you think?