B3. Farmer Jože has a square lawn in front of his barn, 10 meters long. Since he doesn't like mowing the grass, he tied a goat to the lawn.

a) Where and how long a rope did he tie the goat to so that it can graze the most grass without crossing the boundary? Mark it on a sketch to scale $1: 200$.

b) How many square meters of grass did the goat graze? Round the result to one decimal place.

c) What percentage of the lawn could the goat not graze? Round the result to one decimal place.
B3. a) The sketch of the lawn is a square with a side of $5 \mathrm{~cm}$. The farmer tied the goat to the midpoint of the diagonal of the square with a rope. The rope is $5 \mathrm{~m}$ long.

![](https://cdn.mathpix.com/cropped/2024_06_07_e0eaf7053b4419cdf2d7g-8.jpg?height=523&width=514&top_left_y=338&top_left_x=882)

b) The goat has grazed $S=\pi \cdot 5^{2}=78.5 \mathrm{~m}^{2}$ of the lawn.

c) The goat has not grazed $10^{2}-\pi \cdot 5^{2}=21.5 \mathrm{~m}^{2}$ of the lawn, which represents $21.5 \%$ of the entire lawn with an area of $100 \mathrm{~m}^{2}$.

## Scoring: Total: 5 points

a) A square with a side of $5 \mathrm{~cm}$ is drawn.

The goat is tied with a $5 \mathrm{~m}$ long rope,

b) The goat has grazed $78.5 \mathrm{~m}^{2}$ of the lawn. . ................................................................ (If the contestant did not consider rounding, no points are awarded.)

c) The goat could not graze $21.5 \%$ of the lawn.

(If the contestant did not consider rounding, no points are awarded.)