Solid angle a solid angle in steradians is the following ratio: where A is the spherical surface area and r is the radius of the considered sphere. Solid angles are often used in physics, in particular astrophysics. The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance. Here "area" means the area of the object when projected along the viewing direction. The solid angle of a sphere measured from any point in its interior is 4 sr, and the solid angle subtended at the center of a cube by one
Surface area but not on its position and orientation in space. This means that surface area is invariant under the group of Euclidean motions. These properties uniquely characterize surface area for a wide class of geometric surfaces called "piecewise smooth". Such surfaces consist of finitely many pieces that can be represented in the parametric form with a continuously differentiable function formula_4 The area of an individual piece is defined by the formula Thus the area of "S" is obtained by integrating the length of the normal vector formula_6 to the surface over the appropriate region "D" in the parametric "uv" plane. The