Question

the radius of a circle is 49 miles. what is the circles area?
round your answer to the nearest hundredth.
square miles

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

Given \( r = 49 \) miles, substitute \( r \) into the formula: \( A=\pi\times(49)^2 \).
First, calculate \( 49^2 = 49\times49 = 2401 \).
Then, \( A=\pi\times2401 \approx 3.14159\times2401 \).

Step3: Calculate the numerical value

\( 3.14159\times2401 = 3.14159\times2400 + 3.14159\times1 = 7539.816+3.14159 = 7542.95759 \).

Step4: Round to the nearest hundredth

Rounding \( 7542.95759 \) to the nearest hundredth (two decimal places), we look at the third decimal place, which is 7. Since \( 7\geq5 \), we round up the second decimal place. So \( 7542.95759\approx7542.96 \).

Answer:

7542.96