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

The maximum diameter of hemishere = Side of cubical block (a) = 7 cm
Radius of hemisphere = a/2 = 3.5 cm
The surface are of the soild
= Surface area of cubical block + CSA of hemisphere – Area of base of hemisphere
= 6a² + 2πr² – πr²
= 6a² + πr²
= 6 × 7² + 22/7 × 3.5² = 294 + 38.5 = 332.5 cm²
Hence, the surface area of the solid is 332.5 cm²