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 r2 - π r2
= 6(edge)2 + π r2
Total surface area of solid
=6(7)2 +22/7 x 3.5 x 3.5
= 294 +38.5