For a sphere S of radius r, one possible parametrization is:
x = r sin u cos v
y = r sin u sin v
z = r cos u
0 <= u <= pi
0 <= v <= 2 pi
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Since a sphere is round it is a shape without a face.
A sphere has no corners, it is a 3-D circle.
It is incorrect to say that sphere has lateral area. First sphere do not have sides like other geometric figure. In fact a line or plane can intersect the surface of a sphere in just one point. Sphere has no lateral side. It is enough to say surface area of sphere than lateral surface area of the sphere.
Sphere.
A ball has the shape known in mathematics as a sphere. (Unless it's an American football.)