Q 9. The approximate shape is a square.  As it's not quite a whole square,  you estimated it's area at about 95 square feet.

Q10.  Is spot on.  But round it off.  (i) because part of the calculation is an estimate so 7 decimal places is way over the top and (ii) the calculation is  to say what area of grass the goat can reach.  So how accurate do you need to be anyway?  The actual amount the goat gets will depend on other factors like the quality of the grass (it may be better in one place than another) and how far the goat is prepared to stretch to reach that deliciously succulent bit etc etc.  7 decimal places would amount to tiny fractions of a single blade of grass.

I'm going to log out for a while.  I'll check in again later on.

Bob

Yes that looks good to me.

Your answer for Q9 is a little less than one full square, which you estimate as 95.

Then the long calculation is for Q10.

The question for Q8 doesn't actually make sense so to cover all possible angles on this I would answer it a bit like this:

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?

Initially the radius is 50 again; then dropping to 30 and finally to 10.  The answers are exactly the same as when the goat went round the first way.

The 3/4 part (radius = 50)  is the same as before and so the non-overlapping bit for this is zero.

The 1/4 part (radius = 30) is the same but it does overlap a little with the answer already obtained.

If what I've said makes sense to you, I would prefer that you put it into your own words rather than just copy me. That way you can hold your head up and say you did this rather than being accused of just copying.

I think that is the end of the whole thing.  Hurrah!!

Bob

6. How much of the 50 foot circle can the goat reach without getting interrupted by the barn? What is that area?

6. 3/4 * 50^2 * PI= 1875 PI

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?

7- 30 is the new radius. It can make 1/4. The area is 1/4 * 30² * 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?

8. the radius is 30. It can make 1/4 the area is 1/4 * 30² * 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?
9. 95. They look like 3 triangles uniting. the area is

(3/4 * 50^2 * PI= 1875 PI + 1/4 * 30² * PI = 225 PI + 1/4 * 30² * PI = 225 PI) - 95
2325PI - 95 = 7209.2020292


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

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

3/4 +1/4= 4/4

50^2 + 30^2 = 80^2

4/4 * 80 ^2 * PI = 6400 PI

Thanks

YES!! 

That's what I've got too.

Well done.

Bob

hi zee-f

Oh dear.  A bit of a muddle.  You had the correct yellow area back in post 81.

Also remember in post 79 you had a good estimate of the answer by counting squares.  I said then, I thought it was a bit high.  So you should not be satisfied untill you land up with an answer that is somewhere between these two.

Let me set out for you what you should be calculating.

step 1.  area of yellow quadrants = 3/4 x 50^2 x PI   =

step 2.  area of red quadrant       = 1/4 x 30^2 x PI   =

step 3.  area of green quadrant    = same answer       =

step 4   estimated area (overlap)                               = 95

step 5. add up 1, 2 and 3 and take away 4          total =

Please set it out like this then, if there is still a gremlin lurking in there, I can see where it is. 

Bob

Bob