Write the area A of a circle as a function

Question

Write the area A of a circle as a function

vakirnarhh 2021-11-25 Answered

Write the area A of a circle as a function of its circumference C.

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Lupe Kirkland

Answered 2021-11-26 Author has 21 answers

Step 1
Equation for the circumference of a circle.

C = 2 π r

Step 2
Equation for the area of a circle.

A = π r^{2}

Step 3
Solve for r in terms of C.

C = 2 π r

r = \frac{C}{2 π}

Step 4
Plug in the equation for r in terms of C into the equation for the area.

A = π r^{2}

A = π {(\frac{C}{2 π})}^{2}

A = \frac{C^{2}}{4 π}

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Abel Maynard

Answered 2021-11-27 Author has 19 answers

Area of a circle

= A = (π) r^{2}

Circumference of a circle

= C = 2 (π) r

Where pi is a constant and r is the radius of the circle.
Using these two formulas we can express A in terms of C as follows:

C^{2} = {[2 (π) r]}^{2}

\Rightarrow C^{2} = 4 [{(π)}^{2}] r^{2}

\Rightarrow C^{2} = 4 (π) [(π) r^{2}]

As

(π) r^{2} = A

\Rightarrow C^{2} = 4 (π) A

Therefore:

A = \frac{C^{2}}{4 (π)}

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