A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter of the hemisphere can have? Find the surface area of the solid?

The greatest diameter that a hemisphere can have = 7 cm .

Surface area of the solid after surmounted hemisphere

\( = \ 6 l^2 \ - \ \pi R^2 \ + \ 2 \pi R^2 \)

\(= \ 6l^2 \ + \ \pi R^2 \)

\( = \ 6(7)^2 \ + \ \frac{22}{7} \ × \ ( \frac{7}{2} )^2 \)

\( = \ 6 \ × \ 49 \ + \ 11 \ × \ \frac{7}{2} \)

\( = \ 294 \ + \ 38.5 \ = \ 332.5 \) cm²