# What would the area of a circle be if the circumference is 20pi?

Aug 1, 2015

=color(blue)(314cm^2

#### Explanation:

The circumference of a circle is given by formula:
color(blue)(2pir

So, $2 \pi r = 20 \pi$

$2 \cancel{\pi} r = 20 \cancel{\pi}$

$r = \frac{20}{2}$

$r = 10 c m$(assuming the units to be in $c m$)

The area of a circle is given by formula:
color(blue)(pir^2

Where,
$\pi$ has a constant value of $\approx 3.14$
and $r$ denotes the radius.

The radius of the circle $= 10 c m$

The area $= \pi {r}^{2} \approx 3.14 \times {\left(10\right)}^{2}$

$= 3.14 \times \left(100\right)$

=color(blue)(314cm^2