You did not go wrong anywhere. Your answer is just an approximation. The exact answer requires calculus.

Check the drawing out. The black are is what is impossible for the goat to reach.

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7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: The new radius is 30. It can make up to ¼. So the area would be:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI) = 706.858

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: The radius is 30. It can make up to ¼. So the area would be:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI) = 706.858

9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?

Answer: I would say that the area is 75. It looks like it almost makes a square shape.

10. What is the total grazing area the goat can reach?

Answer: To get this answer, I added up the ansers of #6, #7 and #8 then subtracted the answer from #9:

1875(PI) + 225(PI) + 225(PI) 75

2325(PI) 75

7304.202 75

7229.202 is the final answer.

7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI)

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: (this would be the same as #7)

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI)

9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?

Answer:

3/4 x 10^2 x PI

3/4 x 100 x PI

75 (PI)

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If these are right, shall we move on to #10?

That is what I would put also but the solution I have is 300 π. Let's go with your answer.

But take a look at this thread that bob bundy worked on

http://www.mathisfunforum.com/viewtopic … =18391&p=6

before and after post 117. This problem has been worked on in this forum. I also posted the exact answer for 10) in the computer math thread.

It does agree with Bob's work there.

Am going offline for a bit.

]]>3/4 x 10^2 x PI

3/4 x 100 x PI

75 (PI) is the final answer or 235.619

And #7 and #8 are literally asking for the same thing. So the equation for them both would be:

1/4 x 30^2 x PI

1/4 x 900 x PI

225 (PI) is the final answer or 706.858 - is this correct?

Yes, that is what I would put down as the answer.

]]>This would be the equation for #9?

]]>1/4 x 10^2 x PI

Am I following the right path here?

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