2005 PMWC Problems/Problem T7

Problem

Skipper’s doghouse has a regular hexagonal base that measures one metre on each side. Skipper is tethered to a 2-metre rope which is fixed to a vertex. What is the area of the region outside the doghouse that Skipper can reach? Calculate an approximate answer by using $\pi=3.14$ or $\pi=22/7$ .

Solution

[geogebra]8adbc5cf46e8c80136a021d43648b8653cfbf839[/geogebra]

The big sector has a radius of 2 and is 2/3 of the total circle that it used to be a part of, and thus has an area of $4\pi*\frac{2}{3}=\frac{8}{3}\pi$ . The two little sectors each have radius 1 and are 1/6 the total area of their circle, so the area of each of those is $\frac{\pi}{6}$ . Adding, we get $\frac{8}{3}\pi+\frac{\pi}{6}+\frac{\pi}{6}=3\pi$ . Then approximate.

2005 PMWC (Problems)
Preceded by [[2005 PMWC Problems/Problem {{{num-b}}}\|Problem {{{num-b}}}]]	Followed by Problem T8
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2005 PMWC Problems/Problem T7

Problem

Solution

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