# How do you find the area of a circle if the circumference of a circle is 28.26cm?

May 24, 2018

${\text{area "~~63.55" cm}}^{2}$

#### Explanation:

$\text{the area (A) of a circle is given by}$

•color(white)(x)A=pir^2larrcolor(blue)"r is the radius"

$\text{to calculate A we require to find r}$

$\text{the circumference (C) of a circle is given by}$

•color(white)(x)C=2pir

$\text{here "C=28.26 " so equating}$

$2 \pi r = 28.26$

$\text{divide both sides by } 2 \pi$

$\frac{\cancel{2 \pi} r}{\cancel{2 \pi}} = \frac{28.26}{2 \pi}$

$r = \frac{28.26}{2 \pi} \leftarrow \text{ round on final step}$

$\text{substitute this value into formula for A}$

$A = \pi \times {\left(\frac{28.26}{2 \pi}\right)}^{2} \approx 63.55 \text{ to 2 dec. places}$