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

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.

$C=2\pi r$

Step 2

Equation for the area of a circle.

$A=\pi {r}^{2}$

Step 3

Solve for r in terms of C.

$C=2\pi r$

$r=\frac{C}{2\pi}$

Step 4

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

$A=\pi {r}^{2}$

$A=\pi {\left(\frac{C}{2\pi}\right)}^{2}$

$A=\frac{{C}^{2}}{4\pi}$

Equation for the circumference of a circle.

Step 2

Equation for the area of a circle.

Step 3

Solve for r in terms of C.

Step 4

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

Abel Maynard

Answered 2021-11-27
Author has **19** answers

Area of a circle $=A=\left(\pi \right){r}^{2}$

Circumference of a circle$=C=2\left(\pi \right)r$

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:

$C}^{2}={\left[2\left(\pi \right)r\right]}^{2$

$\Rightarrow {C}^{2}=4\left[{\left(\pi \right)}^{2}\right]{r}^{2}$

$\Rightarrow {C}^{2}=4\left(\pi \right)\left[\left(\pi \right){r}^{2}\right]$

As$\left(\pi \right){r}^{2}=A$

$\Rightarrow {C}^{2}=4\left(\pi \right)A$

Therefore:$A=\frac{{C}^{2}}{4\left(\pi \right)}$

Circumference of a circle

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:

As

Therefore:

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