Subject: can you help with the maths behind an explanation of lightdilutinginasphere

the book that i am reading right now quotes this, ''imagine a lightbulb 
illuminating a room. the light spreads out in a sphere. the strength of the 
light is diluted across this sphere. thus, if you double the radius of the 
sphere, then the light is spread out over the sphere with four times the area. 
IN GENERAL IF A LIGHT BULB EXISTS IN N DIMENSIONAL SPACE, THEN ITS LIGHT IS 
DILUTED ACROSS A SPHERE WHOSE AREA INCREASES AS THE RADIUS IS RAISED TO THE 
N-1 POWER. could you explain the maths behind the statement in bold letters. 
the book is called PARALLEL UNIVERSES By MICHIO KAKU. Thankyou!

Re: can you help with the maths behind an explanation of lightdilutinginasphere