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Partially illuminated cylinder (Posted on 2021-11-03) Difficulty: 3 of 5
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?

  Submitted by Jer    
Rating: 5.0000 (1 votes)
Solution: (Hide)
The edge of the illuminated portion, when unrolled follows four portions of the curve y=5arccos(x/5) from 0 to 5. (0 being the center, 5 the right.)

Turning sideways the curve becomes x=5cos(y/5). This integral from 0 to 5pi/2 equals 25. The whole area is thus 100.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle AnswerK Sengupta2024-02-04 09:37:08
Some Thoughtsre(3): SolutionBrian Smith2021-11-13 11:10:58
Hints/Tipsre(2): SolutionBrian Smith2021-11-08 10:21:56
re: SolutionJer2021-11-07 16:19:08
SolutionSolutionBrian Smith2021-11-04 11:58:43
re(2): Possible Solutionbroll2021-11-04 08:45:31
re: Possible SolutionJer2021-11-04 06:56:26
Possible Solutionbroll2021-11-03 22:07:10
solnSteven Lord2021-11-03 08:02:58
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