Since, the diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm.

radius = r = 7/2 cm

It’s curved surface area = 2 πr^{2} = 2 x 22/7 x 7/2 x 7/2 = 77 cm^{2} …… (i)

Now,

Surface area of the top of the resulting solid = Surface area of the top face of the cube – Area of the base of the hemisphere

Surface area of the cube = 5 x (side)^{2} = 5 x 49 = 245 cm^{2} …… (iii)

Hence,

Total area of resulting solid = 245 + 10.5 + 77 = 332.5 cm^{2}