Given data:
The diameter of the cut sphere, D=14 in.
The radius of the cut sphere is,

The cut sphere is called a hemisphere.
The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.