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 Partially illuminated cylinder (Posted on 2021-11-03)
A cylinder with base radius 5 and height 10 is sitting on a table. A spotlight with a cylindrical beam of radius 5 is shining directly at the cylinder. The beam is parallel to the table and the bottom of the beam just touches the table. The cylinder just barely blocks the entire light beam.

What is the illuminated area?

 See The Solution Submitted by Jer Rating: 5.0000 (1 votes)

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 re: Solution | Comment 6 of 9 |
(In reply to Solution by Brian Smith)

Your final answer is the area of half of the entire cylinder.  So it's clearly too large.

Your function needs an absolute value sign.  The way it is, it's letting the light pass through the cylinder and illuminate the back side at the top.  A sort-or wrap-around effect for the top half.

Either that or integrate just the bottom half of the circle {x=0 to 5} and double the result.

 Posted by Jer on 2021-11-07 16:19:08

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