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.