Question

the diameter of a circle is 84.6 meters. what is the circles area? round your answer to the nearest hundredth. square meters

Explanation:

Step1: Find the radius

The radius \( r \) of a circle is half of its diameter \( d \). Given \( d = 84.6 \) meters, so \( r=\frac{d}{2}=\frac{84.6}{2} = 42.3 \) meters.

Step2: Calculate the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Substitute \( r = 42.3 \) into the formula: \( A=\pi\times(42.3)^{2}\). Calculate \( (42.3)^{2}=42.3\times42.3 = 1789.29 \). Then \( A=\pi\times1789.29\approx3.14159\times1789.29\approx5620.58 \) (rounded to the nearest hundredth).

Answer:

\( 5620.58 \) square meters