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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

thank you

5 answers

To find the area of a circle, you can use the formula:

\[ \text{Area} = \pi r^2 \]

where \( r \) is the radius of the circle. Given that the radius \( r \) is 2.1 miles and using \( \pi \approx 3.14 \):

\[ \text{Area} = 3.14 \times (2.1)^2 \]

First, calculate \( (2.1)^2 \):

\[ (2.1)^2 = 4.41 \]

Now, substitute this value back into the area formula:

\[ \text{Area} = 3.14 \times 4.41 \]

Now multiply:

\[ 3.14 \times 4.41 \approx 13.8384 \]

Rounding to the hundredths place, the area of the circle is approximately:

\[ \text{Area} \approx 13.84 \text{ square miles} \]

So, the estimated area of the circle is 13.84 square miles.

2.1 x 2 = 4.2, not 4.41

I apologize for the oversight in the calculation. You are correct that the square of 2.1 should be calculated as follows:

\[ (2.1)^2 = 2.1 \times 2.1 = 4.41 \]

However, the multiplication should be verified for clarity. Here's the correct step-by-step calculation for the area:

  1. Calculate \( (2.1)^2 \): \[ 2.1 \times 2.1 = 4.41 \]

  2. Now, use \( \pi \approx 3.14 \) to find the area: \[ \text{Area} = 3.14 \times 4.41 \]

  3. Performing the multiplication: \[ 3.14 \times 4.41 = 13.8384 \]

  4. Finally, rounding to the hundredths place gives us: \[ \text{Area} \approx 13.84 \text{ square miles} \]

Thus, the calculated area of the circle with a radius of 2.1 miles is indeed approximately 13.84 square miles. Thank you for your patience!

im quite sure the answer is 13.188, estimated to be 13.19.

Let’s carefully go through the calculation again to ensure accuracy.

To find the area \(A\) of a circle, we use the formula:

\[ A = \pi r^2 \]

where \(r\) is the radius.

Given:

  • \(r = 2.1\) miles
  • \(\pi \approx 3.14\)
  1. First, calculate \(r^2\):

\[ (2.1)^2 = 2.1 \times 2.1 = 4.41 \]

  1. Now, multiply by \(\pi\):

\[ A = 3.14 \times 4.41 \]

  1. Performing the multiplication:

    • \(3.14 \times 4.41\) can be calculated step-by-step: \[ 3.14 \times 4.41 = 13.8384 \]

Rounding \(13.8384\) to the hundredths place gives \(13.84\), not \(13.19\).

If you are arriving at \(13.188\), please double-check your calculations for the specific products and rounding. The calculations for the area of a circle using the provided values are accurate as displayed.

Final answer: The area is approximately 13.84 square miles.