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?
If the cylinder was a flat sheet, the footprint of the spotlight would be a circle.
As the paper is folded away from the light, the illuminated height, a, stays the same, but the width, b, increases to form an ellipse.
In the stated problem, the illuminated width will be exactly half the circumference of the cylinder.
An ellipse is just a generalised circle, with area pi*a*b, where a and b are the semimajor and semiminor axes. In this case, b is (5*pi)/2 and a is 5.
So the area is 12.5pi^2, or around 123.4 units.
Edited on November 3, 2021, 10:33 pm
Posted by broll
on 2021-11-03 22:07:10