A cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid(in cm2 ).
The hemisphere surmounts the cube, the maximum diameter the hemisphere can have = side of cube as shown in the figure below. The hemisphere will just touch the sides of top face of the cube.
Therefore, maximum diameter Hemisphere can have = 7 cm
⇒ Radius of Hemisphere = r = 72=3.5 cm
Surface area of solid = Surface area of 5 Faces of cube + Surface area of Hemisphere + Surface area left uncovered on the top face of the cube (shown in blue)
=5l2+2.π.r2+ Area of Square ABCD - Area of inscribed circle in square ABCD
∴ The surface area of combined solid = 332.5 cm2