Question

the radius of a circle is 13 metres. what is the circles area? round your answer to the nearest hundredth. square metres

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 \( r = 13 \) metres. Substituting \( r = 13 \) into the formula, we get \( A=\pi\times(13)^{2} \).

Step3: Calculate \( (13)^{2} \)

First, calculate \( 13^{2}=13\times13 = 169 \). So now the formula becomes \( A=\pi\times169 \).

Step4: Compute the value using \( \pi\approx3.14159 \)

Using the approximation \( \pi\approx3.14159 \), we have \( A = 3.14159\times169 \). Calculate \( 3.14159\times169 = 530.92911 \).

Step5: Round to the nearest hundredth

Rounding \( 530.92911 \) 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 \( 530.92911\approx530.93 \).

Answer:

\( 530.93 \)