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Last Halloween, a farmer in Idaho harvested a very large spherical pumpkin. He cut off a segment of the pumpkin equal to 1/4 of its circumference. If the weight of that segment was 5 kg, then what was the weight of the pumpkin? Thanks for any help.

 Jun 30, 2019
 #1
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Hectictar: I can't and don't know how to draw a picture of a square inside a circle, but you most certainly can. Assume this circle contains the diameter of the pumpkin with a radius = 1. One side of the square can be the chord that will form the segment. Bisect the 4 right angle of the square, and where they intersect, is the center of the circle.
The segment should subtend an angle of 90 degrees at center of the circle. Find the area of the segment, which comes to =0.2853982....sq.units. Since this area is proportional to 5 kg weight and is proportional to pi, or the area of the entire circle, which is proportional to the weight "W" of the pumpkin.
In other words: W =pi / 0.2853982 * 5 =~55 kg - the weight of the pumpkin.

 Jun 30, 2019
 #2
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Very Curious, George!  How is that you can post a moderately complex solution, but do not know how to post an image?

Why did you address this to Hectictar?

 

Here’s a much better Halloween Story, by Dragonlance.  The kid is a gifted writer.  He’s not a kid anymore: he’s attending university on an academic scholarship.   It’s very cool to see someone grow up on this forum. smiley

 Jun 30, 2019

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