Finding Surface Area of Sphere with Illuminated Light Question

[zachem62]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

I have NO idea how to do this problem. Please help! Thanks!

 

[berkeman]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

I have NO idea how to do this problem. Please help! Thanks!

Start by drawing a diagram of the setup...

 

[zachem62]

Start by drawing a diagram of the setup...

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

 

[berkeman]

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

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.

 

[HallsofIvy]

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

 

[LCKurtz]

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

 

[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

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.