Final answer:
The angle made by an area of a sphere at its center is called a solid angle, measured in steradians (sr). However, the given information is not sufficient to determine the solid angle.
Step-by-step explanation:
The angle made by an area of a sphere at its center equal to 2 times the square of its radius is known in the field of mathematics as a solid angle. The solid angle is measured in steradians (sr), which is the three-dimensional equivalent of the radian used for planar angles. Given the information that the angle is equivalent to 2 times the square of its radius, we can deduce that we are dealing with an area equal to the surface area of a sphere covered by a solid angle of 2 steradians, because the surface area of a complete sphere is 4π times the square of its radius, and a complete sphere encompasses a solid angle of 4π steradians.
Therefore, with the given information, the correct answer is c. 2 steradian.