Question

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?

Answer 1

whats the radius?

Answer 2

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

Answer 3

@alekos

Answer 4

@Michele_Laino can you help me with this question :)

Answer 5

have you been given an answer?

Answer 6

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

Answer 7

I think that your problem can be represented like below:

Answer 8

O.o

Answer 9

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

Answer 10

oops..\(OP=4\)

Answer 11

then \(OS=2-1=1\)
and hence the requested surface is:
\(2 \cdot \pi \; \cdot OQ \;HS=2 \;\cdot \pi\;\cdot 2\;\cdot 1=4\;\pi\)

Answer 12

thank you thank you thank you ^_^

Answer 13

:)

Answer 14

oops.. I meant \(HS=OS-OH=2-1=1\)