I need help solving equations of circles (8th grade Math homework). the closer the value is to 1, the more circular the lake is. Formula = L — 2√(pi)π*A -The length of crater lake's shorline is about 26mi and is area is about 21. solve -suppose a lake is perfectly circular and has a 2 mi diameter. solve -evaluate the expression for 2 other perfectly circular lakes. you choose diameters. what do you see? -evaluate the expression for the lake of the ozarks. the length of shorline is 1350 and area is 93. solve

Expert Answers

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When dealing with a perfect circle (in your case, a hypothetical lake), then the following applies:

Circle Circumference = C

Circle Diameter = d

Circle Radius = d/2 or r

Circle Area = A


Circumference (C) = pi * (d)

A = pi * (r)^2

Therefore, attempting to interpret the formula in your question, the following is offered:

For a perfectly circlular lake, L = C = pi * d

Finding L (or C) when area of the circle is given, A, follows:

A = pi * r^2, and r = square root (A / pi)

L = pi * d = pi * 2r = pi * 2* square root (A / pi)


L = 2 * square root (A * pi)

Now, getting back to the equation:

L - 2 * square root (A* pi) = 0 for a perfectly round lake.

Let's try your questions with the crater lake having L = 26 and A =21:

26 - 2 * square root (21 * pi) = 26 - 16.2 = 9.75  and not equal to zero, and not a perfect circlular lake. 

For a perfect circle with circumference = 18.849, then area (from equations above) = 28.27

18.849 - 2 * square root (28.27 * pi) = 0 and therefore, a perfect circle. 



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