SOLUTION: A circular field contains 10 acres. Determine length of fence to enclose the field. Area of circle; pi * r^2. Circumference of circle; pi * diameter. Acre = 43560 sq. ft.

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Question 1089642: A circular field contains 10 acres. Determine length of fence to enclose the field.
Area of circle; pi * r^2.
Circumference of circle; pi * diameter.
Acre = 43560 sq. ft.
Not sure how to proceed. Non-homework.
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
10%2Aacres%2A43560%28ft%5E2%2Facre%29=pi%2Ar%5E2
pi%2Ar%5E2=435600
r=sqrt%28435600%2Fpi%29
-
Fence length for perimeter (circumference), 2%2Api%2Asqrt%28435600%2Fpi%29.
Compute or simplify.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


10_acres+=+%2810_acres%29%2A%28%2843560_sq_ft%29%2F%281_acre%29%29

10_acres+=+435600_sq_ft

note how the "acres" units cancel.

There are 435600 sq ft in 10 acres

The area of the circular field is 435600 square feet

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Use this area value to find the radius

Area of circle = pi*(radius)^2
A = pi*r^2
435600 = pi*r^2
435600/pi = (pi*r^2)/pi
435600/pi = r^2
r^2 = 435600/pi
sqrt(r^2) = sqrt(435600/pi)
r = 372.365125 ... use a calculator for this step

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The radius of the circle is approximately 372.365125 feet

Now that we know the radius, we can compute the circumference C

C = 2*pi*r
C = 2*pi*372.365125
C = 2,339.639082 ... use a calculator for this step

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You'll need roughly 2,339.639082 feet of fencing

Rounded to the nearest whole number, you'll need 2,340 feet of fencing