perplexus.info :: Calculus : Partially illuminated cylinder

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.

Comments: ( You must be logged in to post comments.)

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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