Question

the radius of a circle is 16 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 is \( A=\pi r^{2} \), where \( r \) is the radius of the circle.

Step2: Substitute the given radius into the formula

We are given that the radius \( r = 16 \) kilometers. Substituting \( r = 16 \) into the formula, we get \( A=\pi\times(16)^{2} \).

Step3: Calculate the value

First, calculate \( 16^{2}=256 \). Then, multiply by \( \pi \): \( A = 256\pi \). Using a calculator to approximate \( \pi\approx3.14159265 \), we have \( A\approx256\times3.14159265 \).
\( 256\times3.14159265 = 804.247712 \).

Step4: Round to the nearest hundredth

Rounding \( 804.247712 \) to the nearest hundredth (two decimal places), we look at the third decimal place which is 7. Since \( 7\gt5 \), we round up the second decimal place. So \( 804.247712\approx804.25 \).

Answer:

\( 804.25 \)