Question

A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 3 yards long. The shed is a 4 yard by 6 yard shed. Calculate the area of grass that the goat can eat

Answer 1

We can visualize the situation as a rectangle (the shed) with a circle (the area the goat can reach) extending out from one corner. The diameter of the circle is the length of the rope, which is 3 yards. We can use the Pythagorean theorem to calculate the radius of the circle:

radius^2 = (3/2)^2 + (4/2)^2
radius^2 = 2.25 + 4
radius^2 = 6.25
radius = sqrt(6.25) = 2.5 yards

So the area of the circle that the goat can reach is:

A = πr^2
A = π(2.5)^2
A ≈ 19.63 square yards

Therefore, the area of grass that the goat can eat is approximately 19.63 square yards.