Consider a hollow sphere of radius R, in which a light source is placed at its centre. A square plate of side length S is held in place within the sphere by a pole of length L units. The square plate's position is then such that the displacement between the centre of the square and the light source is RL units.
The square plate is also oriented in a way such that an imaginary line drawn perpendicular to the surface of the plate and passing through the plate's centre will pass through the light source.
Determine the surface area of the shadow formed on the spherical shell, due to the square plate.
(In reply to
Solution by Bractals)
See correction in later post. Bractals' formula is correct.
Using Bractal's formula:
DECLARE FUNCTION acos! (x!)
DECLARE FUNCTION asin# (x#)
DEFDBL AZ
DIM SHARED pi
pi = ATN(1) * 4
CLS
DO
INPUT "r,s,l:", r, s, l
a = 2 * r ^ 2 * (2 * acos(s * s / (s ^ 2 + 4 * (r  l) ^ 2))  pi)
PRINT a
LOOP
DEFSNG AZ
FUNCTION acos (x)
s = SQR(1  x * x)
acos = ATN(s / x)
END FUNCTION
DEFDBL AZ
FUNCTION asin (x)
c = SQR(1  x * x)
asin = ATN(x / c)
END FUNCTION
gives
r,s,l:1,.2,.4
12.45824939409365
r,s,l:2,.3,.5
50.10706450142342
Definitely shouldn't be negative, and disagrees calculations using my formula.
Edited on August 20, 2009, 12:30 am

Posted by Charlie
on 20090819 19:29:41 