What is the unit for a solid angle?

What is the unit for a solid angle?

• A. Degree (°)
• B. Radian (rad)
• C. Steradian (sr)
• D. Turn (turn)

Answer: (C)

The unit for a solid angle is the steradian (sr). A solid angle is a three-dimensional analog of a two-dimensional angle and is defined as the ratio of the area on the surface of a sphere to the square of the radius of that sphere. One steradian is the solid angle that, subtended at the center of a sphere, covers an area equal to the square of the sphere's radius. To give some context, while degrees and radians are units for measuring planar (two-dimensional) angles, they are not suitable for solid angles. Degrees measure the circular angle defining a portion of a circle, and radians are defined similarly in terms of the arc length relative to the radius of the circle. The concept of a turn, which describes a complete rotation around a point, also pertains to planar angles rather than the three-dimensional nature of solid angles. Ultimately, the steradian effectively captures the relationship between a surface area and a sphere's volume, making it the correct and appropriate unit for solid angles.

The unit for a solid angle is the steradian (sr). A solid angle is a three-dimensional analog of a two-dimensional angle and is defined as the ratio of the area on the surface of a sphere to the square of the radius of that sphere. One steradian is the solid angle that, subtended at the center of a sphere, covers an area equal to the square of the sphere's radius.

To give some context, while degrees and radians are units for measuring planar (two-dimensional) angles, they are not suitable for solid angles. Degrees measure the circular angle defining a portion of a circle, and radians are defined similarly in terms of the arc length relative to the radius of the circle. The concept of a turn, which describes a complete rotation around a point, also pertains to planar angles rather than the three-dimensional nature of solid angles.

Ultimately, the steradian effectively captures the relationship between a surface area and a sphere's volume, making it the correct and appropriate unit for solid angles.