Question

the radius of a circle is 27 kilometers. what is the circles area? round your answer to the nearest hundredth. square kilometers

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 \( r = 27 \) kilometers. Substituting \( r = 27 \) into the formula, we get \( A=\pi\times(27)^{2} \).

Step3: Calculate \( 27^{2} \)

First, calculate \( 27^{2}=27\times27 = 729 \). So now the area is \( A=\pi\times729 \).

Step4: Use the value of \( \pi\approx3.14159 \) to compute the area

Using \( \pi\approx3.14159 \), we have \( A\approx3.14159\times729 \).
Calculating \( 3.14159\times729 \):
\( 3.14159\times729 = 3.14159\times(700 + 29)=3.14159\times700+3.14159\times29 \)
\( 3.14159\times700 = 2199.113 \)
\( 3.14159\times29=3.14159\times(30 - 1)=3.14159\times30-3.14159\times1 = 94.2477 - 3.14159 = 91.10611 \)
Adding these two results: \( 2199.113+91.10611 = 2290.21911 \)

Step5: Round to the nearest hundredth

Rounding \( 2290.21911 \) to the nearest hundredth (two decimal places), we look at the third decimal place which is 9. Since \( 9\gt5 \), we round up the second decimal place. So \( 2290.21911\approx2290.22 \).

Answer:

\( 2290.22 \)