Question

A square barn measures 40 feet on each side.
A goat is tethered outside by a rope that is
attached to one corner of the barn:

a. Suppose that the length of the rope is 28 feet. On how many square meters of land is the goat able to graze? What shape is formed?

Answer 1

Answer:

$160.175 m^{2}$ and shape is a sector with a central angle 90 degrees

Step-by-step explanation:

Since the goat is tied to the corner of the square barn, the goat will be able to graze on $\frac {28 ft}{40 ft}=0.7$ of the circle with radius 28 ft outside the barn. To convert 28 ft to m since we want answer in square meters, we know that 1 ft=0.3048 hence 28 ft= 28*0.3048=8.5344 m

$Area=\pi r^{2}= 0.7\times \pi\times (8.5344 m)^{2}=160.1746932 m^{2}$

The shape that the grazing goat will form is a sector with a central angle 90 degrees