It took me about a minute and a half to solve this problem, which I saw on YouTube:
In the comments, leave your answer in terms of pi, or use a calculator to give an answer in 4 decimal places (please round).
For confirmation, go watch the video, which offers two solutions: a simple solution involving commonsense geometry, and an unnecessarily complex solution involving higher math.* One of the commenters to the video notes that even sixth-grade Chinese kids might have trouble solving this. Since I used to tutor this stuff, though, I found it easy. Every once in a while, it's good to flex the brain muscles by doing little math problems like this.
(My handwritten solution is here.)
*CORRECTION: the video actually goes on to consider a substantially more complicated problem: how to calculate the irregularly shaped area of one corner of the figure. That's a different animal altogether, and that's what I get for watching the video in my office with the audio off! Serves me right.
100-25pi
ReplyDeleteTook me less than a minute because I immediately saw the shortcut:
ReplyDeleteThe simplification (which allows you to dispense with paper and pencil) is to notice that if you twist the diagonal to the vertical, the answer pops out as:
The area of one of the squares minus the area of one of the circles.