A goat is tied with 1 vertex of a shed with the distance of 10m.Find out how much distance the goat can grace around the shed?
Think of the rope as the radius of the circle. But he can only get 3/4 of the circle because the shed corner takes up a quarter of the circles area. So use (pi)(r)(r) to find the area of the circle then multiply by 0.75 and you have the grazing distance the goat can go (assuming he does not eat his way through the rope... and go to the next farmers field : )
how big is the shed?
To find out how much distance the goat can graze around the shed, we need to consider the length of the rope that it is tied with. In this case, the rope is 10 meters long.
The rope is attached to 1 vertex of the shed, so the goat can move freely in the shape of a circle with the shed as the center and the rope length (10 meters) as the radius.
To calculate the distance the goat can graze around the shed, we need to find the circumference of this circular area.
The circumference of a circle is given by the formula:
C = 2πr
Where C is the circumference, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the radius is 10 meters, so we can plug in the values:
C = 2 * 3.14159 * 10
Now we can calculate the circumference:
C = 20 * 3.14159
C ≈ 62.8318
So, the goat can graze around the shed for approximately 62.8318 meters.