The given problem asks to estimate the area of a circle using the formula for the area, $A = \pi r^2$, where $r$ is the radius of the circle. The problem specifies rounding all values to the nearest whole number before substitution.

Steps to solve:

1. Given radius: $r = 11.3$ cm.

   • Rounded to the nearest whole number: $r \approx 11$ cm.

2. Use the formula: $A = \pi r^2$ Substitute $r = 11$: $A = \pi \times 11^2 = \pi \times 121$

3. Approximate the area: Using $\pi \approx 3.14$, $A \approx 3.14 \times 121 = 379.94 \text{ square centimeters}.$

4. Rounded result: The area is approximately $380 \, \text{cm}^2$.

Final Answer:

The estimated area of the circle with radius 11.3 cm is approximately 380 cm².

Do you want more details or have any questions?

Here are some related questions:

1. How would the area change if the radius was not rounded?
2. What would the area be if the radius was 12 cm instead?
3. How can we estimate the circumference of the circle using this radius?
4. What is the percentage error in rounding the radius before calculating the area?
5. How would the result change if a more accurate value for $\pi$ was used?

Tip: When estimating areas with formulas like $A = \pi r^2$, rounding early may introduce small errors, so check how significant they are for precision.