Wood pile perimeter
Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...
Three touching circles have an interesting area between them...
Problem
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![Wood Pile Perimeter Wood Pile Perimeter](/sites/default/files/styles/large/public/thumbnails/content-id-7181-Wood%252520Pile%252520Perimeter%252520Stefania.png?itok=OxbSI4Ak)
The diagram shows three touching circles each of radius $5$cm and a line which touches two of them.
Find, in terms of $\pi$, the total perimeter of the two shaded shapes.
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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![Wood Pile Perimeter Wood Pile Perimeter](/sites/default/files/styles/large/public/thumbnails/content-id-7181-Weekly%2525202011%252520-%25252030%252520Solution.png?itok=2OIrsciL)
The straight part is the same length as two radii, so is $10\text{cm}$ long.
The perimeter of the shaded shapes is therefore $10+10\pi\text{cm}$.