1. Mar 14, 2012

### zachem62

1. The problem statement, all variables and given/known data

Find the surface area of a sphere of radius R that is illuminated by a light that is held h units away from its surface.

2. Relevant equations

integral surface area formula i don't know how to type it up properly on here.

3. The attempt at a solution

2. Mar 14, 2012

### Staff: Mentor

Start by drawing a diagram of the setup...

3. Mar 14, 2012

### zachem62

I've already drawn a diagram I just couldn't put it up here thats all.

4. Mar 14, 2012

### Staff: Mentor

There are several ways to post your diagram and show your work. What format is it in? If hand-drawn, can you scan it or snap a picture of it on your phone? If it is in Visio or other drawing program, convert it to PDF (like using PrimoPDF) and attach it to your reply.

5. Mar 14, 2012

### HallsofIvy

Draw lines from the light tangent to the sphere. That gives you the illuminated area.

6. Mar 14, 2012

### LCKurtz

Also think about a cross-section and treating it as a surface of revolution.

7. Mar 19, 2012

### zhandele

I'm not entirely sure where you encounter difficulty?

A lot of people get stuck for a time on arc length and surface integrals (I did). If that's it, maybe this link will help:

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-partial-fractions-integration-by-parts-arc-length-and-surface-area/session-79-surface-area/MIT18_01SCF10_Ses79b.pdf [Broken]

If that's clear, then you just need to figure out where to put the lower limit on the definite integral. Try drawing a diagram and look for similar triangles. I'm including two attachments, pdf files I made myself.

I wonder if I could just attach that MIT file ... it's being distributed freely anyway.

#### Attached Files:

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• ###### MIT18_01SCF10_Ses79b.pdf
File size:
165.9 KB
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Last edited by a moderator: May 5, 2017