conversion of radius, radians to steradians of cone?

If the angle at the vertex in any cross section through the axis of a cone is (2 theta) then the solid angle at the vertex is 2 pi (1 - cos theta) steradians.

Hello Josh, thanks for giving me a right platform to explain the normal doubts that the beginners would have regarding. First let us relate the radian concept and the degree concept. You just draw a circle on a paper with some radius say 10 cm. Now using thread of length 10 cm place it on the circumference of that circle and mark the extreme points of the thread. Say AB is the arc length. Now the angle subtended by this arc AB will be taken as one radian. Because the angle subtended by the arc is got by dividing the arc length by the radius r. Here AB and r of the same length 10 cm. If so then how much will be the angle subtended by the whole circumference of the circle at its centre? It is assigned to be 2pi. Because the circumference is 2pi r and radius is r. Dividing arc length by radius, we get 2 pi. Is it not? But the value of pi is irrational one and hence man for convenience to do the calculation has brought degree concept into the scene assigning 2 pi to be 360 degree. Hence pi equals to 180 degree. Now the tips to jump over from radian to degree or degree to radian. If degree is given first divide by equivalent degree namely by 180 to make it a mere number. Then multiply by equivalent radian pi. You will get it in radian. Example say you would like to convert 30 degree in radian. First divide it by 180 degree, you get 1/6 without any unit. Now multiply by pi you get pi/6. So 30 degree is equivalent to pi/6 radian. Same way you want to change pi/12 radian into degree. First divide by pi so that it becomes a mere number ie 1/12. Now multiply by equivalent 180 degree so we get, 15 degree. Now in your problem, radius r = 0.25" and arc length s = 0.5". Hence the angle at the centre by this arc will be theta(in radian) = s/r = 0.5/0.25 = 2 radian. If you need this value in degree divide by pi and then multiply by 180 degree. So the angle in degree will be 360/pi degree. Most important point the actual value of pi is 3.14 of course approximately. The value of pi is not 180 degree. Of course the equivalent value of pi radian in degree may 180. Note the crucial difference, friend. Hence plugging 3.14 for pi in 360/pi we get, 114.65 degree nearly So what you have got is absolutely correct friend. Congrats.

Steradians