Question

the radius of a circle is 30.2 miles. what is the circles area? r=30.2 mi round your answer to the nearest hundredth. square miles submit

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle with radius \( r \) is \( A = \pi r^2 \).

Step2: Substitute the given radius into the formula

We are given that \( r = 30.2 \) miles. Substituting this into the formula, we get \( A=\pi\times(30.2)^2 \).
First, calculate \( (30.2)^2 \): \( 30.2\times30.2 = 912.04 \).
Then, multiply by \( \pi \): \( A=\pi\times912.04\approx3.14159\times912.04 \).

Step3: Calculate the numerical value

\( 3.14159\times912.04 = 3.14159\times900 + 3.14159\times12.04 = 2827.431+37.8247436 = 2865.2557436 \).

Step4: Round to the nearest hundredth

Rounding \( 2865.2557436 \) to the nearest hundredth (two decimal places), we look at the third decimal place, which is 5. Since 5 is greater than or equal to 5, we round up the second decimal place. So \( 2865.2557436\approx2865.26 \).

Answer:

\( 2865.26 \)