wat is a steradian?

Question

can anyone explain it, how we get 1 sr =r*r

Answer 1

A radian is defined as the angle that cuts off an arc with length 1 from the unit circle.
Because the unit circle has circumference 2 pi, a radian is 1/(2 pi) part of a full planar angle.

A steradian is defined as the solid angle (in space) that cuts off a part of the unit sphere with surface area 1.
Because the unit sphere has area 4 pi, a steradian is 1/(4 pi) part of a full solid angle.

The formula 1 sr = r * r does not make sense.

Even if you would cut out a "rectangle" of the unit sphere with sides of 1 radian, defined by the parallels and meridians at +/- 1/2 rad around the equator, you would not get a steradian. The area would be equal to

INT (1 rad * cos a) da with angle a from -1/2 rad to +1/2 rad
=
2 sin (1/2 rad) = 0.95885

so 1 radian * 1 radian would equal 0.95885 steradians.

Answer 2

unit of solid-angle measure in the International System of Units (SI), defined as the solid angle of a sphere subtended by a portion of the surface whose area is equal to the square of the sphere's radius. Since the complete surface area of a sphere is 4p times the square of its radius, the total solid angle about a point is equal to 4p steradians. Derived from the Greek for solid and the English word radian, a steradian is, in effect, a solid radian; the radian is an SI unit of plane-angle measurement defined as the angle of a circle subtended by an arc equal in length to the circle's radius.

Answer 3

It is one of the ways of expressing solid angle. It is the standard international unit for solid angle.

Answer 4

It is solid angle of one radian.