From the figure, it can be observed that the greatest diameter possible for such hemisphere is equal to the cube’s edge, i.e., 7cm.

Radius (r) of hemispherical part = 7/2=3.5

Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part

= 6(edge)^{2} + 2π r^{2} - π r^{2}

= 6(edge)^{2} + π r^{2}

Total surface area of solid

=6(7)2 +22/7 x 3.5 x 3.5

= 294 +38.5

=332.5cm2