The circumference $C$ of a circle is related to its radius $r$ by the formula:

$C = 2\pi r$

We are given that the circumference is $22\pi$ meters, so we can write:

$22\pi = 2\pi r$

Dividing both sides of the equation by $2\pi$, we get:

$r = \frac{22\pi}{2\pi} = 11 \, \text{meters}$

Now that we know the radius $r = 11 \, \text{meters}$, we can use the formula for the area $A$ of a circle:

$A = \pi r^2$

Substituting the value of $r = 11$ meters and $\pi \approx 3.14$, we get:

$A = 3.14 \times (11)^2 = 3.14 \times 121 = 379.94 \, \text{square meters}$

So, the approximate area of the circle is 379.94 square meters.

Would you like more details on this calculation? Here are 5 related questions to explore further:

1. What happens to the area if the radius were doubled?
2. How would the circumference change if the radius were halved?
3. How does the value of $\pi$ affect the accuracy of the area and circumference?
4. What is the relationship between the diameter and the circumference of a circle?
5. How do you calculate the area if only the circumference is given without using the value of $\pi$?

Tip: Always round intermediate results when possible to avoid rounding errors in the final answer.