Question
What is the area of a circle with a radius of 2.1 miles? Estimate the area to the hundredths place using 3.14 for π. Solve using the formula for the area of a circle, A=πr^2.
Answers
GPT-4o mini
To find the area of a circle using the formula \( A = \pi r^2 \), we will substitute \( r = 2.1 \) miles and use \( \pi \approx 3.14 \).
1. First, calculate \( r^2 \):
\[
r^2 = (2.1)^2 = 2.1 \times 2.1 = 4.41
\]
2. Next, multiply this result by \( \pi \):
\[
A = \pi r^2 = 3.14 \times 4.41
\]
3. Now, perform the multiplication:
\[
3.14 \times 4.41 = 13.8384
\]
Finally, we round this to the hundredths place:
\[
A \approx 13.84 \text{ square miles}
\]
Therefore, the estimated area of the circle is \( \boxed{13.84} \) square miles.
1. First, calculate \( r^2 \):
\[
r^2 = (2.1)^2 = 2.1 \times 2.1 = 4.41
\]
2. Next, multiply this result by \( \pi \):
\[
A = \pi r^2 = 3.14 \times 4.41
\]
3. Now, perform the multiplication:
\[
3.14 \times 4.41 = 13.8384
\]
Finally, we round this to the hundredths place:
\[
A \approx 13.84 \text{ square miles}
\]
Therefore, the estimated area of the circle is \( \boxed{13.84} \) square miles.