Area of circle whose circumference is 34pi?

Question

solomonzelman · Answer

area of the circle is given by the following formula:
(where ${\rm A}$ denotes the area, and $\rm r $ denotes the radius)

$ {\rm A} = \pi {\rm r}^2$

solomonzelman · Answer

the circumference of the circle is given by the formula:
${\rm C}=2\pi{\rm r}$

(where $\rm C$ denotes the circumference, and $ {\rm r}$ denotes the radius)

solomonzelman · Answer

so, you can do this:

${\rm C}=2\pi {\rm r}$

$\displaystyle \frac{\rm C}{2\pi}= {\rm r}$

(solving for r in terms of C)

and then plug it into the area formula.

$\displaystyle \rm A=\pi {\rm r}^2$

$\displaystyle \rm A=\pi \left( \frac{\rm C}{2\pi} \right)^2$

$\displaystyle \rm A=\pi \cdot \frac{\rm C^2}{4(\pi^2)} $

$\displaystyle \rm A=\frac{\rm C^2}{4\pi} $

solomonzelman · Answer

So we have shown that Area in term of the circumference is:

$\displaystyle \rm A=\frac{\rm C^2}{4\pi} $

solomonzelman · Answer

now, you can plug your circumference that you are given.

$\displaystyle \rm A=\frac{\rm (34\pi)^2}{4\pi} $

solomonzelman · Answer

continue from here.

anonymous · Answer

Thank you! :)

solomonzelman · Answer

yw