A sphere of radius is illuminated by a light source that is 4m away from the sphere's center. What is the surface area of the sphere that is brightened?

Question

alekos · Answer

whats the radius?

anonymous · Answer

oh sorry i forgot , it's 2m :)

anonymous · Answer

@alekos

anonymous · Answer

@Michele_Laino  can you help me with this question :)

alekos · Answer

have you been given an answer?

anonymous · Answer

no but theses are the choices : a. pi b. 2 pi c 4 pi d 6pi

michele_laino · Answer

I think that your problem can be represented like below:
|dw:1449329457572:dw|

anonymous · Answer

O.o

michele_laino · Answer

we have $PQ=4$, $OQ=2$, Then, using the 2-nd theorem of Euclid, we get $OH=1$

michele_laino · Answer

oops..$OP=4$

michele_laino · Answer

|dw:1449329674321:dw|
then $OS=2-1=1$
and hence the requested surface is:
$2 \cdot \pi \; \cdot OQ \;HS=2 \;\cdot \pi\;\cdot 2\;\cdot 1=4\;\pi$

anonymous · Answer

thank you thank you thank you ^_^

michele_laino · Answer

:)

michele_laino · Answer

oops.. I meant $HS=OS-OH=2-1=1$