# What is the area of a circle with a circumference of 56.52 inches (in.)? Use 3.14 forimage.

Jun 5, 2018

$\approx 254 {\text{in}}^{2}$

#### Explanation:

${C}_{\text{circle}} = 2 \pi r$

$56.52 = 2 \pi r$

$28.26 = \pi r$

$r = \frac{28.26}{\pi} \approx 8.995$

${A}_{\text{circle}} = \pi {r}^{2}$

${A}_{\text{circle}} = \pi {\left(8.995\right)}^{2} \approx 254.19$

We can combine the formulas:

$C = 2 \pi r$

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

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

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

Now we have a formula for the area of a circle of any given circumference:

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

$C = 56.52$

$A = {56.52}^{2} / \left(4 \pi\right) \approx 254.19$

Jun 5, 2018

$254.34 {\text{in}}^{2}$

#### Explanation:

$\therefore \text{circumference of a circle} = 2 \pi r$

$\therefore 2 \pi r = 56.52 \text{in}$

$\therefore r = \frac{56.52}{2 \pi}$

$\therefore r = \frac{56052}{2 \times 3.14}$

$\therefore r = \frac{56.52}{6.28}$

$\therefore r = 9$

$\therefore \text{Area of a circle} = \pi {r}^{2}$

$\therefore A = 3.14 \times {9}^{2}$

$\therefore A = 254.34 {\text{in}}^{2}$