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## Quiz of the Month (June 2006)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  22/7     ( = 3.1428571 ...)
2.  333/106  ( = 3.1415094 ...)
3.  355/113  ( = 3.1415929 ...)
```

Notes.

Easily solved by means of a computer program (using variables of suitable precision).

Alternatively, using a pocket calculator, multiply PI by n with n = 1, 2, 3, ... , and whenever the result is close to an integer m (either above or below), test m/n - PI.

For example, PI * 113 = 354.999969 ...
And 355/113 - PI = 0.00000027 ..

#### THIS MONTH'S QUIZ

A square barn with sides of length 12 m stands in the middle of a large field. A goat is tethered by a rope to the mid-point of one side of the barn. Find the area of field which the goat can graze if the length of the rope is:

1. 6 m

2. 18 m

3. 30 m

***