What different types of companionship exist

11-32. the main character in the parable, the forgiving father, whose character remains constant throughout the story, is a picture of god. in telling the story, jesus identifies himself with god in his loving attitude to the lost. the younger son symbolizes the lost (the tax collectors and sinners of that day, luke 15: 1), and the elder brother represents the self-righteous (the pharisees and teachers of the law of that day, luke 15: 2). the major theme of this parable seems not to be so much the conversion of the sinner, as in the previous two parables of luke 15, but rather the restoration of a believer into fellowship with the father. in the first two parables, the owner went out to look for what was lost (luke 15: 1-10), whereas in this story the father waits and watches eagerly for his son's return. we see a progression through the three parables from the relationship of one in a hundred (luke 15: 1-7), to one in ten (luke 15: 8-10), to one in one (luke 15: 11-32), demonstrating god’s love for each individual and his personal attentiveness towards all humanity. we see in this story the graciousness of the father overshadowing the sinfulness of the son, as it is the memory of the father’s goodness that brings the prodigal son to repentance (romans 2: 4).

the answer is

r ≈5.641

plug in the area of 100 yards into the equation

100=

divide each side by pi

≈ 31.8309=

take the square root of each side to find r

=r

r ≈5.641