Question

1. A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 2 yards long and a plane view (from above) of the shed and field is shown below. Use this information for Parts A and B below.
Part A: Calculate the area of grass that the goat can eat.
Part B: What length of rope would enable the goat to eat 30 square yards of grass? Show all your reasoning.

Answer 1

Answer:

Step-by-step explanation:

Step one:

Given data

the length of the rope =2yards----the radius

(Note that the goat can only move in a circular path)

the area the goat can eat is the area of the circle it can cover

1. A= πr^2

A=3.142*2^2

A=3.142*4

A=12.57square yards

Step two:

given that the area A=30 square yards

we want to solve for the radius r

A= πr^2

30=3.142*r^2

r^2=30/3.142

r^2=9.55

r=√9.55

r=3.09 yard

The length is approximately 3 yards