Math CentralQuandaries & Queries


Question from Ken, a parent:

I jog around a circular 20 acre lake. Please help me learn the distance of the perimeter of the lake so I will know my jogging distance. Thanks

Hi Ken.

Recall the circle's relationships:
C = 2πr
A = πr2

You have A and want C, so we rewrite the second equation:
r = √(A/π)

Now substitute that into the first equation:
C = √(4πA)

Acres is unwieldy, so we need to convert it to a squared length unit.
I'm in Canada so I'll convert to square meters. An acre is 80 937 square
meters. If you want other units, just do the conversion you like, then
substitute in like this:
C = √(4π[80 937])
C = √(1017083)
C = 1008.5 meters

So the answer is slightly over a kilometer.

Hope this helps,
Stephen La Rocque.


Hello Ken,

The perimeter of a circle is given a different name, circumference.  The formula for the circumference of a circle is, C = 2πr, where r is the radius.  Thus we need to determine the radius of the lake.

If the lake is 20 acres in area then converting we get 80937 square meters.  The formula for the area of a circle is A = πr2 so we have

80937 = πr2

r ≈ 160.5 meters.

Plugging into the circumference formula yields,

C = 2π (160.5) ≈ 1008.5 meters.


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