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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?

 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.

 Subject Author Date Puzzle Answer K Sengupta 2024-02-04 09:37:08 re(3): Solution Brian Smith 2021-11-13 11:10:58 re(2): Solution Brian Smith 2021-11-08 10:21:56 re: Solution Jer 2021-11-07 16:19:08 Solution Brian Smith 2021-11-04 11:58:43 re(2): Possible Solution broll 2021-11-04 08:45:31 re: Possible Solution Jer 2021-11-04 06:56:26 Possible Solution broll 2021-11-03 22:07:10 soln Steven Lord 2021-11-03 08:02:58

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