Answers to Mind Games on the Web

Vol 1, No 4 Answers Presented by Smart Science ™ and Bill Graham as a free service for entertainment and education
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ANSWER TO
DOBBIN AND A CHICKEN COOP

by Bill Graham

First you need a good diagram of the area that Dobbin can reach with the chicken coop built on his pasture.

solution to dobbin and chicken coop This diagram shows that Dobbin has three-fourths of his original circular pasture plus, on the right, a small quarter circle with a radius of 5 yards (yellow) and a larger quarter circle at the bottom with a radius of 15 yards (red). The formula for the area of a circle is

A = πr² The area of his new grazing space consists of the three parts. ¾π25² = 1875π/4
¼π5² = 25π/4
¼π15² = 225π/4 Add the three areas together to get 2125π/4.

The original grazing area was 25²π = 625π. To get the fractional part of the original area, divide the new area by the original area. Note that the πs cancel out.

2125π/4 ÷ 625π = 17/20 = 0.85 or 85% That is a 15% reduction in Dobbin's eating space. I wouldn't like my meals to be cut back by 15% either.

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